TheInfoList

Tides are the rise and fall of
sea level Mean sea level (MSL) (often shortened to sea level) is an average In colloquial, ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in th ...

s caused by the combined effects of the
gravitational Gravity (), or gravitation, is a natural phenomenon by which all things with mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an ...

forces exerted by the
Moon The Moon is Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distri ...

and the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

, and the
rotation A rotation is a circular movement of an object around a center (or point) of rotation. The plane (geometry), geometric plane along which the rotation occurs is called the ''rotation plane'', and the imaginary line extending from the center an ...
of the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

.
Tide table Tide tables, sometimes called tide charts, are used for tidal prediction The theory of tides is the application of continuum mechanics Continuum mechanics is a branch of mechanics Mechanics (Ancient Greek, Greek: ) is the area of physi ...
s can be used for any given locale to find the predicted times and
amplitude The amplitude of a ic is a measure of its change in a single (such as or ). There are various definitions of amplitude (see below), which are all s of the magnitude of the differences between the variable's . In older texts, the of a period f ...

(or "
tidal range Tidal range is the height difference between high tide and low tide (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the Moon an ...
"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the
amphidromic An amphidromic point, also called a tidal node, is a geographical location which has zero tidal amplitude The amplitude of a Periodic function, periodic Variable (mathematics), variable is a measure of its change in a single Period (mathematics), ...
systems of the oceans, and the shape of the coastline and near-shore
bathymetry Bathymetry (pronounced ) is the study of underwater depth of ocean floor The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
(see ''
Timing Timing is the time when something happens or the spacing of events in time. "Timing" also means the tracking of time when an event is happening in time. Good timing is having waited for the right moment to match parts that belong together. Timing m ...
''). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience
semi-diurnal A diurnal cycle (or diel cycle) is any pattern that recurs every 24 hours as a result of one full rotation of the planet Earth around its axis. Earth's rotation causes surface temperature fluctuations throughout the day and night, as well as sea ...
tides—two nearly equal high and low tides each day. Other locations have a
diurnal Diurnal ("daily Daily or The Daily may refer to: Journalism * Daily newspaper A newspaper is a Periodical literature, periodical publication containing written News, information about current events and is often typed in black ink with a ...
tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides vary on timescales ranging from hours to years due to a number of factors, which determine the
lunitidal interval The lunitidal interval measures the time lag from lunar culmination In observational astronomy, culmination is the instant of time of the transit of a astronomical object, celestial object (the Sun, the Moon, a planet, a star, constellation or a ...
. To make accurate records,
tide gauge A tide gauge is a device for measuring the change in sea level relative to a vertical datum. It its also known as mareograph, marigraph, sea-level recorder and limnimeter. Operation Sensors continuously record the height of the water level with ...

s at fixed stations measure water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the reference (or datum) level usually called
mean sea level There are several kinds of mean in mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and thei ...
. While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forces such as wind and barometric pressure changes, resulting in
storm surge A storm surge, storm flood, tidal surge, or storm tide is a coastal flood Coastal flooding normally occurs when dry and low-lying land is submerged by seawater. The range of a coastal flooding is a result of the elevation of floodwater that penet ...

s, especially in shallow seas and near coasts. Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field that varies in time and space is present. For example, the shape of the solid part of the Earth is affected slightly by
Earth tide Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...
, though this is not as easily seen as the water tidal movements.

# Characteristics

Tide changes proceed via the two main stages: * The water stops falling, reaching a
local minimum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ra ...
called low tide. * The water stops rising, reaching a
local maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ra ...

called high tide. In some regions, there are additional two possible stages: * Sea level rises over several hours, covering the
intertidal zone The intertidal zone, also known as the foreshore or seashore, is the area above water level Water level, also known as gauge height or stage, is the elevation of the free surface of a sea, stream, lake or reservoir relative to a specified ve ...
; flood tide. * Sea level falls over several hours, revealing the intertidal zone; ebb tide. Oscillating
currents Currents or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stream), c ...
produced by tides are known as tidal streams or
tidal currents (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the Moon and tides have a phase shift In physics and mathematics, the phase of a ...
. The moment that the tidal current ceases is called ''
slack water Slack water is a short period in a body of tidal water when the water is completely unstressed, and there is no movement either way in the tidal stream, and which occurs before the direction of the tidal stream reverses. Slack water can be estim ...
'' or ''slack tide''. The tide then reverses direction and is said to be turning. Slack water usually occurs near high water and low water, but there are locations where the moments of slack tide differ significantly from those of high and low water. Tides are commonly ''semi-diurnal'' (two high waters and two low waters each day), or ''diurnal'' (one tidal cycle per day). The two high waters on a given day are typically not the same height (the daily inequality); these are the ''higher high water'' and the ''lower high water'' in
tide table Tide tables, sometimes called tide charts, are used for tidal prediction The theory of tides is the application of continuum mechanics Continuum mechanics is a branch of mechanics Mechanics (Ancient Greek, Greek: ) is the area of physi ...
s. Similarly, the two low waters each day are the ''higher low water'' and the ''lower low water''. The daily inequality is not consistent and is generally small when the Moon is over the
Equator The Equator is a circle of latitude, about in circumference, that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the N ...

.

## Reference levels

The following reference tide levels can be defined, from the highest level to the lowest: * ''Highest astronomical tide'' (HAT) – The highest tide which can be predicted to occur. Note that meteorological conditions may add extra height to the HAT. * ''
Mean high water springs Mean high water springs (MHWS) is the averaged highest level that spring tide (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the ...
'' (MHWS) – The average of the two high tides on the days of spring tides. * ''Mean high water neaps'' (MHWN) – The average of the two high tides on the days of neap tides. * ''
Mean sea level There are several kinds of mean in mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and thei ...
'' (MSL) – This is the average sea level. The MSL is constant for any location over a long period. * ''Mean low water neaps'' (MLWN) – The average of the two low tides on the days of neap tides. * ''
Mean low water springs The average of the levels of each pair of successive low waters during that period of about 24 hours in each semi-lunation (approximately every 14 days), when the range of the tide is greatest (Spring Range). See also * Mean high water springs R ...
'' (MLWS) – The average of the two low tides on the days of spring tides. * ''
Lowest astronomical tide A chart datum is the water level Water level, also known as gauge height or stage, is the elevation of the free surface of a sea, stream, lake or reservoir A reservoir (; from French language, French ''réservoir'' ) is most commonly an ...
'' (LAT) – The lowest tide which can be predicted to occur.

# Tidal constituents

''Tidal constituents'' are the net result of multiple influences impacting tidal changes over certain periods of time. Primary constituents include the Earth's rotation, the position of the Moon and Sun relative to the Earth, the Moon's altitude (elevation) above the Earth's Equator, and
bathymetry Bathymetry (pronounced ) is the study of underwater depth of ocean floor The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
. Variations with periods of less than half a day are called ''harmonic constituents''. Conversely, cycles of days, months, or years are referred to as ''long period'' constituents. Tidal forces affect the entire earth, but the movement of solid Earth occurs by mere centimeters. In contrast, the atmosphere is much more fluid and compressible so its surface moves by kilometers, in the sense of the contour level of a particular low pressure in the outer atmosphere.

## Principal lunar semi-diurnal constituent

In most locations, the largest constituent is the ''principal lunar semi-diurnal'', also known as the ''M2 tidal constituent'' or ''M2 tidal constituent''. Its period is about 12 hours and 25.2 minutes, exactly half a ''tidal lunar day'', which is the average time separating one lunar
zenith The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "high ...

from the next, and thus is the time required for the Earth to rotate once relative to the Moon. Simple s track this constituent. The lunar day is longer than the Earth day because the Moon orbits in the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1:05½ (not at 1:00). The Moon orbits the Earth in the same direction as the Earth rotates on its axis, so it takes slightly more than a day—about 24 hours and 50 minutes—for the Moon to return to the same location in the sky. During this time, it has passed overhead (
culmination In observational astronomy, culmination is the instant of time of the transit of a astronomical object, celestial object (the Sun, the Moon, a planet, a star, constellation or a deep-sky object) across the observer's meridian (astronomy), local me ...
) once and underfoot once (at an
hour angle In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the direction of a point on the celestial sphere. The hour angle of a point is the angle between two planes: one contai ...
of 00:00 and 12:00 respectively), so in many places the period of strongest tidal forcing is the above-mentioned, about 12 hours and 25 minutes. The moment of highest tide is not necessarily when the Moon is nearest to
zenith The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "high ...

or
nadir The nadir (, ; ar, نظير, naẓīr, counterpart) is the direction pointing directly ''below'' a particular location; that is, it is one of two vertical direction In astronomy Astronomy (from el, ἀστρονομία, literally me ...
, but the period of the forcing still determines the time between high tides. Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightly stronger than average force on the side of the Earth facing the Moon, and a slightly weaker force on the opposite side. The Moon thus tends to "stretch" the Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally (see equilibrium tide). As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height. When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called a ''mixed semi-diurnal tide''.

## Range variation: springs and neaps

The semi-diurnal range (the difference in height between high and low waters over about half a day) varies in a two-week cycle. Approximately twice a month, around
new moon In , the new moon is the first , when the and have the same . At this phase, the lunar disk is not visible to the , but its presence may be detected because it stars behind it. The original meaning of the term 'new moon', which is still so ...

and
full moon The full Moon of 22 October 2010, as seen through a lunistice),_so_the_southern_lunar_craters.html" ;"title="lunar_standstill.html" ;"title="ecliptic_coordinate_system.html" "title="Schmidt-Cassegrain telescope. This full Moon was near its nort ...

when the Sun, Moon, and Earth form a line (a configuration known as a syzygy), the
tidal force The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena ...

due to the Sun reinforces that due to the Moon. The tide's range is then at its maximum; this is called the spring tide. It is not named after the
season A season is a division of the year based on changes in weather Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloud cover, cloudy. On Earth, most ...
, but, like that word, derives from the meaning "jump, burst forth, rise", as in a natural
spring Spring(s) may refer to: Common uses * Spring (season), a season of the year * Spring (device), a mechanical device that stores energy * Spring (hydrology), a natural source of water * Spring (mathematics), a geometric surface in the shape of a heli ...
. Spring tides are sometimes referred to as ''syzygy tides''. When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the Earth, and the solar tidal force partially cancels the Moon's tidal force. At these points in the lunar cycle, the tide's range is at its minimum; this is called the neap tide, or neaps. "Neap" is an Anglo-Saxon word meaning "without the power", as in ''forðganges nip'' (forth-going without-the-power). Neap tides are sometimes referred to as ''quadrature tides''. Spring tides result in high waters that are higher than average, low waters that are lower than average, "
slack water Slack water is a short period in a body of tidal water when the water is completely unstressed, and there is no movement either way in the tidal stream, and which occurs before the direction of the tidal stream reverses. Slack water can be estim ...
" time that is shorter than average, and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven-day interval between springs and neaps. File:High tide sun moon same side beginning.png, ''Spring tide:'' Sun and Moon on the same side (0°) File:Low tide sun moon 90 degrees.png, ''Neap tide:'' Sun and Moon at 90° File:High tide sun moon opposite side.png, ''Spring tide:'' Sun and Moon at opposite sides (180°) File:Low tide sun moon 270 degrees.png, ''Neap tide:'' Sun and Moon at 270° File:High tide sun moon same side end.png, ''Spring tide:'' Sun and Moon at the same side (cycle restarts)

## Lunar distance

The changing distance separating the Moon and Earth also affects tide heights. When the Moon is closest, at
perigee Apsis ( el, ἀψίς; plural apsides , Greek: ἀψῖδες; "orbit") denotes either of the two extreme points (i.e., the farthest or nearest point) in the orbit In celestial mechanics, an orbit is the curved trajectory of an phys ...
, the range increases, and when it is at
apogee Apsis ( el, ἀψίς; plural apsides , Greek: ἀψῖδες; "orbit") denotes either of the two extreme points (i.e., the farthest or nearest point) in the of a about its (or simply, "the primary"). The plural term, "apsides," usuall ...

, the range shrinks. Six or eight times a year perigee coincides with either a new or full moon causing
perigean spring tide A proxigean spring tide (also known as a perigean spring tide) is a tide (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the Moo ...
s with the largest ''
tidal range Tidal range is the height difference between high tide and low tide (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the Moon an ...
''. The difference between the height of a tide at perigean spring tide and the spring tide when the moon is at apogee depends on location but can be large as a foot higher.

## Other constituents

These include solar gravitational effects, the obliquity (tilt) of the Earth's Equator and rotational axis, the inclination of the plane of the lunar orbit and the elliptical shape of the Earth's orbit of the Sun. A compound tide (or overtide) results from the shallow-water interaction of its two parent waves.Le Provost, Christian (1991). Generation of Overtides and compound tides (review). In Parker, Bruce B. (ed.) ''Tidal Hydrodynamics.'' John Wiley and Sons,

## Phase and amplitude

Because the ''M''2 tidal constituent dominates in most locations, the stage or ''phase'' of a tide, denoted by the time in hours after high water, is a useful concept. Tidal stage is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are called ''cotidal lines'', which are analogous to
contour lines A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be ...
of constant altitude on topographical maps, and when plotted form a ''cotidal map'' or ''cotidal chart''. High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean, and cotidal lines (and hence tidal phases) advance along the coast. Semi-diurnal and long phase constituents are measured from high water, diurnal from maximum flood tide. This and the discussion that follows is precisely true only for a single tidal constituent. For an ocean in the shape of a circular basin enclosed by a coastline, the cotidal lines point radially inward and must eventually meet at a common point, the
amphidromic point An amphidromic point, also called a tidal node, is a geographical location which has zero tidal for one of the . The (the , or height difference between high tide and low tide) for that harmonic constituent increases with distance from this po ...
. The amphidromic point is at once cotidal with high and low waters, which is satisfied by ''zero'' tidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand,
Iceland Iceland ( is, Ísland; ) is a Nordic Nordic most commonly refers to: * Nordic countries, written in plural as Nordics, the northwestern European countries, including Scandinavia, Fennoscandia and the List of islands in the Atlantic Ocean#N ...

and

.) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constant ''amplitude'' (half the distance between high and low water) which decrease to zero at the amphidromic point. For a semi-diurnal tide the amphidromic point can be thought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high water cotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation, caused by the
Coriolis effect In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...

, is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere. The difference of cotidal phase from the phase of a reference tide is the ''epoch''. The reference tide is the hypothetical constituent "equilibrium tide" on a landless Earth measured at 0° longitude, the Greenwich meridian. In the North Atlantic, because the cotidal lines circulate counterclockwise around the amphidromic point, the high tide passes New York Harbor approximately an hour ahead of Norfolk Harbor. South of Cape Hatteras the tidal forces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines.

# History

## History of tidal theory

Investigation into tidal physics was important in the early development of
celestial mechanics Celestial mechanics is the branch of astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and cel ...
, with the existence of two daily tides being explained by the Moon's gravity. Later the daily tides were explained more precisely by the interaction of the Moon's and the Sun's gravity.
Seleucus of Seleucia Seleucus of Seleucia ( el, Σέλευκος ''Seleukos''; c. 190 BC - c. 150 BC) was a Hellenistic astronomer and philosopher. Coming from Seleucia on the Tigris, Mesopotamia, the capital of the Seleucid Empire, or, alternatively, Seleukia on the Er ...
theorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned in
Ptolemy Claudius Ptolemy (; grc-koi, Κλαύδιος Πτολεμαῖος, , ; la, Claudius Ptolemaeus; AD) was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes ...
's ''
Tetrabiblos ''Tetrabiblos'' () 'four books', also known in Ancient Greek, Greek as ''Apotelesmatiká'' () "Effects", and in Latin as ''Quadripartitum'' "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by th ...
''. In ''De temporum ratione'' (''
The Reckoning of Time ''The Reckoning of Time'' ( la, De temporum ratione) is an Anglo-Saxon era treatise A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerne ...
'') of 725
Bede Bede ( ; ang, Bǣda , ; 672/326 May 735), also known as Saint Bede, The Venerable Bede, and Bede the Venerable ( la, Beda Venerabilis), was an English Benedictine The Benedictines, officially the Order of Saint Benedict ( la, Ordo Sa ...

linked semidurnal tides and the phenomenon of varying tidal heights to the Moon and its phases. Bede starts by noting that the tides rise and fall 4/5 of an hour later each day, just as the Moon rises and sets 4/5 of an hour later. He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides. Bede then observes that the height of tides varies over the month. Increasing tides are called ''malinae'' and decreasing tides ''ledones'' and that the month is divided into four parts of seven or eight days with alternating ''malinae'' and ''ledones''. In the same passage he also notes the effect of winds to hold back tides. Bede also records that the time of tides varies from place to place. To the north of Bede's location (
Monkwearmouth Monkwearmouth is an area of Sunderland, Tyne and Wear in North East England. Monkwearmouth is located at the north side of the mouth of the River Wear. It was one of the three original settlements on the banks of the River Wear along with Bisho ...
) the tides are earlier, to the south later. He explains that the tide "deserts these shores in order to be able all the more to be able to flood other when it arrives there" noting that "the Moon which signals the rise of tide here, signals its retreat in other regions far from this quarter of the heavens". Medieval understanding of the tides was primarily based on works of Muslim astronomers, which became available through Latin translation starting from the 12th century.
Abu Ma'shar Abu Ma'shar, Latinized as Albumasar (also ''Albusar'', ''Albuxar''; full name ''Abū Maʿshar Jaʿfar ibn Muḥammad ibn ʿUmar al-Balkhī'' ; 10 August 787 – 9 March 886, AH 171–272), was an early Persian Muslim astrologer, thought to ...
(d. circa 886), in his ''Introductorium in astronomiam'', taught that ebb and flood tides were caused by the Moon. Abu Ma'shar discussed the effects of wind and Moon's phases relative to the Sun on the tides. In the 12th century,
al-Bitruji Nur ad-Din al-Bitruji (also spelled Nur al-Din Ibn Ishaq al-Betrugi and Abu Ishâk ibn al-Bitrogi) (known in the West by the Latinized name Latinisation (or Latinization) of names, also known as onomastic Latinisation (or Latinization), is the ...
(d. circa 1204) contributed the notion that the tides were caused by the general circulation of the heavens.
Simon Stevin Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as ...
, in his 1608 ''De spiegheling der Ebbenvloet'' (''The theory of ebb and flood''), dismissed a large number of misconceptions that still existed about ebb and flood. Stevin pleaded for the idea that the attraction of the Moon was responsible for the tides and spoke in clear terms about ebb, flood,
spring tide Tides are the rise and fall of sea levels caused by the combined effects of the gravity, gravitational forces exerted by the Moon and the Sun, and the Earth's rotation, rotation of the Earth. Tide tables can be used for any given locale to ...
and
neap tide Tides are the rise and fall of s caused by the combined effects of the forces exerted by the and the , and the of the . s can be used for any given locale to find the predicted times and (or ""). The predictions are influenced by many ...
, stressing that further research needed to be made. In 1609
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe as ...

also correctly suggested that the gravitation of the Moon caused the tides, which he based upon ancient observations and correlations.
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (; 15 February 1564 – 8 January 1642) was an Italian astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the ...

in his 1632 ''
Dialogue Concerning the Two Chief World Systems The ''Dialogue Concerning the Two Chief World Systems'' (''Dialogo sopra i due massimi sistemi del mondo'') is a 1632 Italian-language book by Galileo Galilei comparing the Nicolaus Copernicus, Copernican system with the traditional Ptolemy, Pt ...
'', whose working title was ''Dialogue on the Tides'', gave an explanation of the tides. The resulting theory, however, was incorrect as he attributed the tides to the sloshing of water caused by the Earth's movement around the Sun. He hoped to provide mechanical proof of the Earth's movement. The value of his tidal theory is disputed. Galileo rejected Kepler's explanation of the tides.
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

(1642–1727) was the first person to explain tides as the product of the gravitational attraction of astronomical masses. His explanation of the tides (and many other phenomena) was published in the '' Principia'' (1687) and used his theory of universal gravitation to explain the lunar and solar attractions as the origin of the tide-generating forces. Newton and others before
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French and whose work was important to the development of , , , , , and . He summarized and extended the work of his predecessors in his five-volume (') (1799 ...

worked the problem from the perspective of a static system (equilibrium theory), that provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole Earth. The tide-generating force (or its corresponding
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (phys ...
) is still relevant to tidal theory, but as an intermediate quantity (forcing function) rather than as a final result; theory must also consider the Earth's accumulated dynamic tidal response to the applied forces, which response is influenced by ocean depth, the Earth's rotation, and other factors. In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides.
Daniel Bernoulli Daniel Bernoulli Fellows of the Royal Society, FRS (; – 27 March 1782) was a Swiss people, Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for ...
,
Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ) ...

,
Colin Maclaurin Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-Europ ...
and
Antoine CavalleriAntoine Cavalleri (1698–1765) was a Jesuit professor of mathematics at Cahors Cahors (; oc, Caors ) is a commune in the western part of Southern France. It is the smallest prefecture among the 13 departments that constitute the Occitanie ...
shared the prize. Maclaurin used Newton's theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a
prolate A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating A rotation is a circular movement of an object around a center (or point) of rotation. The plane (geometry), geometric plane along which the rotation occu ...
spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's on motion. Euler realized that the tidal force's ''horizontal'' component (more than the vertical) drives the tide. In 1744
Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanics, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Enc ...
studied tidal equations for the atmosphere which did not include rotation. In 1770
James Cook Captain Captain is a title for the commander of a military unit, the commander of a ship, aeroplane, spacecraft, or other vessel, or the commander of a port, fire department or police department, election precinct, etc. The captain is a milit ...

's
barque A barque, barc, or bark is a type of sailing vessel A sailing ship is a sea-going vessel that uses sails mounted on Mast (sailing), masts to harness the power of wind and propel the vessel. There is a variety of sail plans that propel sailin ...

grounded on the
Great Barrier Reef The Great Barrier Reef is the world's largest coral reef A coral reef is an underwater ecosystems, ecosystem characterized by reef-building corals. Reefs are formed of Colony (biology), colonies of coral polyp (zoology), polyps held tog ...

. Attempts were made to refloat her on the following tide which failed, but the tide after that lifted her clear with ease. Whilst she was being repaired in the mouth of the
Endeavour River The Endeavour River (Guugu Yimithirr language, Guugu Yimithirr: ''Wabalumbaal''), inclusive of the Endeavour River Right Branch, the Endeavour River South Branch, and the Endeavour River North Branch, is a river system located on Cape York Penins ...

Cook observed the tides over a period of seven weeks. At neap tides both tides in a day were similar, but at springs the tides rose in the morning but in the evening. Pierre-Simon Laplace formulated a system of
partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
s relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The Laplace tidal equations are still in use today.
William Thomson, 1st Baron Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British , and born in . at the for 53 years, he did important work in the of electricity and formulation of the first and second , and did much to unify the emergi ...
, rewrote Laplace's equations in terms of
vorticity In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with ...

which allowed for solutions describing tidally driven coastally trapped waves, known as
Kelvin wave A Kelvin wave is a wave In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entitie ...
s. Others including Kelvin and
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officially the French Repu ...
further developed Laplace's theory. Based on these developments and the
lunar theoryLunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbation (astronomy), perturbations) in the Moon's motion, and many attempts have been made to account for them. After centuries of being problemati ...
of E W Brown describing the motions of the Moon,
Arthur Thomas Doodson Dr. Arthur Thomas Doodson (31 March 1890 – 10 January 1968) was a British oceanographer. Early life He was born at Boothstown Boothstown is a Suburban village in Greater Manchester Greater Manchester is a metropolitan county and combi ...
developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies. Some of his methods remain in use.

## History of tidal observation

From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to the Sun and moon.
Pytheas Pytheas of Massalia (; Ancient Greek: Πυθέας ὁ Μασσαλιώτης ''Pythéas ho Massaliōtēs''; Latin: ''Pytheas Massiliensis''; born 350 BC, 320–306 BC) was a Greeks, Greek List of Graeco-Roman geographers, geographer, explore ...
travelled to the
British Isles The British Isles are a group of islands in the North Atlantic off the north-western coast of continental Europe Continental Europe or mainland Europe is the contiguous continent A continent is any of several large landmasse ...

about 325 BC and seems to be the first to have related spring tides to the phase of the moon. In the 2nd century BC, the Hellenistic astronomer
Seleucus of Seleucia Seleucus of Seleucia ( el, Σέλευκος ''Seleukos''; c. 190 BC - c. 150 BC) was a Hellenistic astronomer and philosopher. Coming from Seleucia on the Tigris, Mesopotamia, the capital of the Seleucid Empire, or, alternatively, Seleukia on the Er ...
correctly described the phenomenon of tides in order to support his
heliocentric Heliocentrism is the astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and phenomena. It uses mathematics ...
theory. He correctly theorized that tides were caused by the
moon The Moon is Earth's only natural satellite. At about one-quarter the diameter of Earth (comparable to the width of Australia (continent), Australia), it is the largest natural satellite in the Solar System relative to the size of its plane ...

, although he believed that the interaction was mediated by the
pneuma ''Pneuma'' () is an ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following peri ...
. He noted that tides varied in time and strength in different parts of the world. According to
Strabo Strabo''Strabo'' (meaning "squinty", as in strabismus Strabismus is a condition in which the eyes do not properly align with each other when looking at an object. The eye that is focused on an object can alternate. The condition may be pre ...

(1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the moon's position relative to the Sun. The ''Naturalis Historia'' of
Pliny the Elder #REDIRECT Pliny the Elder #REDIRECT Pliny the Elder#REDIRECT Pliny the Elder Gaius Plinius Secundus (AD 23/2479), called Pliny the Elder (), was a Roman author, a naturalist Natural history is a domain of inquiry involving organisms, includi ...

collates many tidal observations, e.g., the spring tides are a few days after (or before) new and full moon and are highest around the equinoxes, though Pliny noted many relationships now regarded as fanciful. In his ''Geography'', Strabo described tides in the
Persian Gulf The Persian Gulf ( fa, خلیج فارس, translit=xalij-e fârs, lit=Gulf of , ) is a in . The body of water is an extension of the () through the and lies between to the northeast and the to the southwest.United Nations Group of Exper ...
having their greatest range when the moon was furthest from the plane of the Equator. All this despite the relatively small amplitude of
Mediterranean The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin and almost completely enclosed by land: on the north by Western Europe, Western and Southern Europe and Anatolia, on the south by North Africa ...

basin tides. (The strong currents through the
Euripus Strait The Euripus Strait ( el, Εύριπος ) is a narrow channel of water separating the Greek island of Euboea Euboea or Evia ( el, Εύβοια, , ; grc, Εὔβοια, , ) is the second-largest Greek island in area and population, after Cret ...
and the
Strait of Messina The Strait of Messina ( it, Stretto di Messina, Sicilian: Strittu di Missina) is a narrow strait A strait is a naturally formed, narrow, typically navigable waterway that connects two larger bodies of water. Most commonly it is a channel o ...

puzzled
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

.)
Philostratus Philostratus or Lucius Flavius Philostratus (; grc-gre, Φλάβιος Φιλόστρατος; c. 170 – 247/250 AD), called "the Athenian", was a Greek sophist of the Roman Empire, Roman imperial period. His father was a minor sophist of the sa ...
discussed tides in Book Five of ''The Life of
Apollonius of Tyana Apollonius of Tyana ( grc, Ἀπολλώνιος ὁ Τυανεύς; c. 3 BC – c. 97 AD), sometimes also called Apollonios of Tyana, was a Greeks, Greek Neopythagoreanism, Neopythagorean Ancient Greek philosophy, philosopher ...

''. Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the Venerable
Bede Bede ( ; ang, Bǣda , ; 672/326 May 735), also known as Saint Bede, The Venerable Bede, and Bede the Venerable ( la, Beda Venerabilis), was an English Benedictine The Benedictines, officially the Order of Saint Benedict ( la, Ordo Sa ...

described how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along the Northumbrian coast. The first
tide table Tide tables, sometimes called tide charts, are used for tidal prediction The theory of tides is the application of continuum mechanics Continuum mechanics is a branch of mechanics Mechanics (Ancient Greek, Greek: ) is the area of physi ...
in
China China (), officially the People's Republic of China (PRC; ), is a country in East Asia East Asia is the eastern region of Asia Asia () is Earth's largest and most populous continent, located primarily in the Eastern Hemisphere ...

was recorded in 1056 AD primarily for visitors wishing to see the famous
tidal bore Tidal is the adjectival form of tide (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the Moon and tides have a phase shift. Tid ...

in the
Qiantang River The Qiantang River or alternatively Tsientang River is a river A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases a river flows into the ground and becomes dr ...
. The first known British tide table is thought to be that of John Wallingford, who died Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at the
Thames The River Thames ( ), known alternatively in parts as the River Isis, is a river that flows through southern England Southern England, or the South of England, also known as the South, is an area of England consisting of its southernm ...

mouth than upriver at
London London is the capital Capital most commonly refers to: * Capital letter Letter case (or just case) is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowerc ...

. In 1614
Claude d'Abbeville Claude d'Abbeville was a French Franciscan friar of the 17th century, who worked as a missionary with the Tupinambá people, Tupinamba in Maranhao, modern Brazil. He was part of a colonizing party and a mission of four Franciscans sent under a 1611 ...
published the work ''“Histoire de la mission de pères capucins en l’Isle de Maragnan et terres circonvoisines”'', where he exposed that the
Tupinambá people The Tupinambá are one of the various Tupi ethnic groups that inhabit present-day Brazil since before the conquest of the region by Portuguese colonial settlers. In the first years of contact with the Portuguese, the Tupinambás lived in the whole ...
already had an understanding of the relation between the Moon and the tides before Europe. William Thomson (Lord Kelvin) led the first systematic
harmonic analysis Harmonic analysis is a branch of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathe ...
of tidal records starting in 1867. The main result was the building of a
tide-predicting machine A tide-predicting machine was a special-purpose mechanical analog computer of the late 19th and early 20th centuries, constructed and set up to predict the ebb and flow of sea tides and the irregular variations in their heights – which chan ...
using a system of pulleys to add together six harmonic time functions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s. The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the
Thames Estuary The Thames Estuary is where the River Thames The River Thames ( ), known alternatively in parts as the River Isis, is a river that flows through southern England Southern England, or the South of England, also known as the South, ...
. Many large ports had automatic tide gauge stations by 1850. John Lubbock was one of the first to map co-tidal lines, for Great Britain, Ireland and adjacent coasts, in 1840.
William Whewell William Whewell ( ; 24 May 17946 March 1866) was an English English usually refers to: * English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval Eng ...

expanded this work ending with a nearly global chart in 1836. In order to make these maps consistent, he hypothesized the existence of a region with no tidal rise or fall where co-tidal lines meet in the mid-ocean. The existence of such an
amphidromic point An amphidromic point, also called a tidal node, is a geographical location which has zero tidal for one of the . The (the , or height difference between high tide and low tide) for that harmonic constituent increases with distance from this po ...
, as they are now known, was confirmed in 1840 by Captain William Hewett, RN, from careful soundings in the
North Sea The North Sea is a sea The sea, connected as the world ocean or simply the ocean The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
.

# Physics

## Forces

The tidal force produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by the Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Whereas the
gravitational force Gravity (), or gravitation, is a natural phenomenon Types of natural phenomena include: Weather, fog, thunder, tornadoes; biological processes, decomposition, germination seedlings, three days after germination. Germination is th ...
subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance. If the tidal force caused by each body were instead equal to its full gravitational force (which is not the case due to the
free fall #REDIRECT Free fall In Newtonian physics, free fall is any motion of a body where gravity Gravity (), or gravitation, is a list of natural phenomena, natural phenomenon by which all things with mass or energy—including planets, star ...

of the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient is weaker. The tidal force is proportional to :$\text\propto\frac M\propto\rho\left\left(\frac rd\right\right)^3$ where is the mass of the heavenly body, is its distance, ρ is its average density, and is its radius. The ratio is related to the angle subtended by the object in the sky. Since the sun and the moon have practically the same diameter in the sky, the tidal force of the sun is less than that of the moon because its average density is much less, and it is only 46% as large as the lunar. More precisely, the lunar tidal acceleration (along the Moon–Earth axis, at the Earth's surface) is about 1.1 × 10−7 ''g'', while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52 × 10−7 ''g'', where ''g'' is the
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing air drag, drag). This is the steady gain in speed caused exclusively by the force of ''gravitational attraction' ...
at the Earth's surface. The effects of the other planets vary as their distances from Earth vary. When Venus is closest to Earth, its effect is 0.000113 times the solar effect. At other times, Jupiter or Mars may have the most effect. The ocean's surface is approximated by a surface referred to as the
geoid The geoid () is the shape that the ocean The ocean (also the or the world ocean) is the body of that covers approximately 70.8% of the surface of and contains 97% of . Another definition is "any of the large bodies of water into wh ...

, which takes into consideration the gravitational force exerted by the earth as well as
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force A fictitious force (also called a pseudo force, d'Alembert force, or inertial force) is a force that appears to act on a mass whose motion is described using a non-inertial ref ...
due to rotation. Now consider the effect of massive external bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish with distance and cause the ocean's surface to deviate from the geoid. They establish a new equilibrium ocean surface which bulges toward the moon on one side and away from the moon on the other side. The earth's rotation relative to this shape causes the daily tidal cycle. The ocean surface tends toward this equilibrium shape, which is constantly changing, and never quite attains it. When the ocean surface is not aligned with it, it's as though the surface is sloping, and water accelerates in the down-slope direction.

## Equilibrium

The equilibrium tide is the idealized tide assuming a landless Earth. It would produce a tidal bulge in the ocean, with the shape of an ellipsoid elongated towards the attracting body (Moon or Sun). It is ''not'' caused by the vertical pull nearest or farthest from the body, which is very weak; rather, it is caused by the tangent or "tractive" tidal force, which is strongest at about 45 degrees from the body, resulting in a horizontal tidal current.

## Laplace's tidal equations

Ocean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can be modelled using the Laplace tidal equations which incorporate the following features: * The vertical (or radial) velocity is negligible, and there is no vertical
shear Shear may refer to: Textile production * Animal shearing, the collection of wool from various species **Sheep shearing Sheep shearing is the process by which the woollen fleece of a sheep Sheep (''Ovis aries'') are quadruped The zebr ...
—this is a sheet flow. * The forcing is only horizontal (
tangent In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...

ial). * The
Coriolis effect In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...

appears as an inertial force (fictitious) acting laterally to the direction of flow and proportional to velocity. * The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth. As the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively. The boundary conditions dictate no flow across the coastline and free slip at the bottom. The Coriolis effect (inertial force) steers flows moving towards the Equator to the west and flows moving away from the Equator toward the east, allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity.

## Amplitude and cycle time

The theoretical
amplitude The amplitude of a ic is a measure of its change in a single (such as or ). There are various definitions of amplitude (see below), which are all s of the magnitude of the differences between the variable's . In older texts, the of a period f ...

of oceanic tides caused by the Moon is about at the highest point, which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth were rotating in step with the Moon's orbit. The Sun similarly causes tides, of which the theoretical amplitude is about (46% of that of the Moon) with a cycle time of 12 hours. At spring tide the two effects add to each other to a theoretical level of , while at neap tide the theoretical level is reduced to . Since the orbits of the Earth about the Sun, and the Moon about the Earth, are elliptical, tidal amplitudes change somewhat as a result of the varying Earth–Sun and Earth–Moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach . Real amplitudes differ considerably, not only because of depth variations and continental obstacles, but also because wave propagation across the ocean has a natural period of the same order of magnitude as the rotation period: if there were no land masses, it would take about 30 hours for a long wavelength surface wave to propagate along the Equator halfway around the Earth (by comparison, the Earth's
lithosphere A lithosphere ( grc, λίθος [] for "rocky", and [] for "sphere") is the rigid, outermost shell of a terrestrial planet, terrestrial-type planet or natural satellite. On Earth, it is composed of the crust (geology), crust and the portion o ...
has a natural period of about 57 minutes).
Earth tide Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...
s, which raise and lower the bottom of the ocean, and the tide's own gravitational self attraction are both significant and further complicate the ocean's response to tidal forces.

## Dissipation

Earth's tidal oscillations introduce dissipation at an
average In colloquial language, an average is a single number taken as representative of a non-empty list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divide ...

terawatt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...
s. About 98% of this dissipation is by marine tidal movement. Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation. This tidal drag creates torque on the moon that gradually transfers angular momentum to its orbit, and a gradual increase in Earth–moon separation. The equal and opposite torque on the Earth correspondingly decreases its rotational velocity. Thus, over geologic time, the moon recedes from the Earth, at about /year, lengthening the terrestrial day. Day length has increased by about 2 hours in the last 600 million years. Assuming (as a crude approximation) that the deceleration rate has been constant, this would imply that 70 million years ago, day length was on the order of 1% shorter with about 4 more days per year.

## Bathymetry

The shape of the shoreline and the ocean floor changes the way that tides propagate, so there is no simple, general rule that predicts the time of high water from the Moon's position in the sky. Coastal characteristics such as underwater
bathymetry Bathymetry (pronounced ) is the study of underwater depth of ocean floor The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
and coastline shape mean that individual location characteristics affect tide forecasting; actual high water time and height may differ from model predictions due to the coastal morphology's effects on tidal flow. However, for a given location the relationship between lunar
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference and a point or object. The exact definition and reference datum varies according to the context (e.g. ...
and the time of high or low tide (the
lunitidal interval The lunitidal interval measures the time lag from lunar culmination In observational astronomy, culmination is the instant of time of the transit of a astronomical object, celestial object (the Sun, the Moon, a planet, a star, constellation or a ...
) is relatively constant and predictable, as is the time of high or low tide relative to other points on the same coast. For example, the high tide at
Norfolk, Virginia Norfolk ( ) is an independent city An independent city or independent town is a city or town that does not form part of another general-purpose local government entity (such as a province). Historical precursors In the Holy Roman Empire ...
, U.S., predictably occurs approximately two and a half hours before the Moon passes directly overhead. Land masses and ocean basins act as barriers against water moving freely around the globe, and their varied shapes and sizes affect the size of tidal frequencies. As a result, tidal patterns vary. For example, in the U.S., the East coast has predominantly semi-diurnal tides, as do Europe's Atlantic coasts, while the West coast predominantly has mixed tides.U.S. National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (Education section)
map showing world distribution of tide patterns
semi-diurnal, diurnal and mixed semi-diurnal.
Human changes to the landscape can also significantly alter local tides.

# Observation and prediction

## Timing

The tidal forces due to the Moon and Sun generate very long waves which travel all around the ocean following the paths shown in co-tidal charts. The time when the crest of the wave reaches a port then gives the time of high water at the port. The time taken for the wave to travel around the ocean also means that there is a delay between the phases of the Moon and their effect on the tide. Springs and neaps in the
North Sea The North Sea is a sea The sea, connected as the world ocean or simply the ocean The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
, for example, are two days behind the new/full moon and first/third quarter moon. This is called the tide's ''age''. The ocean
bathymetry Bathymetry (pronounced ) is the study of underwater depth of ocean floor The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
greatly influences the tide's exact time and height at a particular
coast The coast, also known as the coastline or seashore, is defined as the area where land meets the ocean The ocean (also the or the world ocean) is the body of that covers approximately 70.8% of the surface of and contains 97% of . Anot ...

al point. There are some extreme cases; the
Bay of Fundy The Bay of Fundy (french: Baie de Fundy) is a bay between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the US state of Maine. It has an extremely high tidal range. The name is likely a corruption of the F ...

, on the east coast of Canada, is often stated to have the world's highest tides because of its shape, bathymetry, and its distance from the continental shelf edge. Measurements made in November 1998 at Burntcoat Head in the Bay of Fundy recorded a maximum range of and a highest predicted extreme of .Charles T. O'reilly, Ron Solvason, and Christian Solomon
"Resolving the World's largest tides"
in J.A Percy, A.J. Evans, P.G. Wells, and S.J. Rolston (Editors) 2005: The Changing Bay of Fundy-Beyond 400 years, Proceedings of the 6th Bay of Fundy Workshop, Cornwallis, Nova Scotia, Sept. 29, 2004 to October 2, 2004. Environment Canada-Atlantic Region, Occasional Report no. 23. Dartmouth, N.S. and Sackville, N.B.
Similar measurements made in March 2002 at Leaf Basin,
Ungava Bay Ungava Bay (french: baie d'Ungava, ; Inuktitut Inuktitut (; , syllabics ; from , "person" + , "like", "in the manner of"), also Eastern Canadian Inuktitut, is one of the principal Inuit languages The Inuit languages are a closely related ...
in northern
Quebec ) , image_shield=Armoiries du Québec.svg , image_flag=Flag of Quebec.svg , coordinates= , AdmittanceDate=July 1, 1867 , AdmittanceOrder=1st, with New Brunswick ("Hope restored") , image_map = New Brunswick in Canada 2.svg , ...

gave similar values (allowing for measurement errors), a maximum range of and a highest predicted extreme of . Ungava Bay and the Bay of Fundy lie similar distances from the continental shelf edge, but Ungava Bay is free of
pack ice Drift ice, also called brash ice, is sea ice that is not attached to the shoreline or any other fixed object (shoals, grounded icebergs, etc.).Leppäranta, M. 2011. The Drift of Sea Ice. Berlin: Springer-Verlag. Unlike fast ice, which is "fastene ...
for about four months every year while the Bay of Fundy rarely freezes.
Southampton Southampton () is a port A port is a maritime law, maritime facility comprising one or more Wharf, wharves or loading areas, where ships load and discharge Affreightment, cargo and passengers. Although usually situated on a sea ...
in the United Kingdom has a double high water caused by the interaction between the ''M''2 and ''M''4 tidal constituents (Shallow water overtides of principal lunar). Isle of Portland, Portland has double low waters for the same reason. The ''M''4 tide is found all along the south coast of the United Kingdom, but its effect is most noticeable between the Isle of Wight and Isle of Portland, Portland because the ''M''2 tide is lowest in this region. Because the oscillation modes of the Mediterranean Sea and the Baltic Sea do not coincide with any significant astronomical forcing period, the largest tides are close to their narrow connections with the Atlantic Ocean. Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan. Elsewhere, as along the southern coast of Australia, low tides can be due to the presence of a nearby Amphidromic point, amphidrome.

## Analysis

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

's theory of gravitation first enabled an explanation of why there were generally two tides a day, not one, and offered hope for a detailed understanding of tidal forces and behavior. Although it may seem that tides could be predicted via a sufficiently detailed knowledge of instantaneous astronomical forcings, the actual tide at a given location is determined by astronomical forces accumulated by the body of water over many days. In addition, accurate results would require detailed knowledge of the shape of all the ocean basins—their
bathymetry Bathymetry (pronounced ) is the study of underwater depth of ocean floor The ocean (also the sea or the world ocean) is the body of salt water which covers approximately 71% of the surface of the Earth.
, and coastline shape. Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by Lord Kelvin, William Thomson. It is based on the principle that the astronomical theories of the motions of Sun and Moon determine a large number of component frequencies, and at each frequency there is a component of force tending to produce tidal motion, but that at each place of interest on the Earth, the tides respond at each frequency with an amplitude and phase peculiar to that locality. At each place of interest, the tide heights are therefore measured for a period of time sufficiently long (usually more than a year in the case of a new port not previously studied) to enable the response at each significant tide-generating frequency to be distinguished by analysis, and to extract the tidal constants for a sufficient number of the strongest known components of the astronomical tidal forces to enable practical tide prediction. The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component. Because astronomical frequencies and phases can be calculated with certainty, the tide height at other times can then be predicted once the response to the harmonic components of the astronomical tide-generating forces has been found. The main patterns in the tides are * the twice-daily variation * the difference between the first and second tide of a day * the spring–neap cycle * the annual variation The ''Highest Astronomical Tide'' is the perigean spring tide when both the Sun and Moon are closest to the Earth. When confronted by a periodically varying function, the standard approach is to employ Fourier series, a form of analysis that uses Sine wave, sinusoidal functions as a ''basis'' set, having frequencies that are zero, one, two, three, etc. times the frequency of a particular fundamental cycle. These multiples are called ''harmonics'' of the fundamental frequency, and the process is termed
harmonic analysis Harmonic analysis is a branch of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathe ...
. If the basis set of sinusoidal functions suit the behaviour being modelled, relatively few harmonic terms need to be added. Orbital paths are very nearly circular, so sinusoidal variations are suitable for tides. For the analysis of tide heights, the Fourier series approach has in practice to be made more elaborate than the use of a single frequency and its harmonics. The tidal patterns are decomposed into many sinusoids having many fundamental frequencies, corresponding (as in the Lunar theory#Results of the theories, lunar theory) to many different combinations of the motions of the Earth, the Moon, and the angles that define the shape and location of their orbits. For tides, then, ''harmonic analysis'' is not limited to harmonics of a single frequency. In other words, the harmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simpler Fourier series approach. Their representation as a Fourier series having only one fundamental frequency and its (integer) multiples would require many terms, and would be severely limited in the time-range for which it would be valid. The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and George Darwin. Arthur Thomas Doodson, A.T. Doodson extended their work, introducing the ''Doodson Number'' notation to organise the hundreds of resulting terms. This approach has been the international standard ever since, and the complications arise as follows: the tide-raising force is notionally given by sums of several terms. Each term is of the form : $A_o \cos\,\left(\omega t + p\right)$ where * is the amplitude. * is the angular frequency, usually given in degrees per hour corresponding to measured in hours. * is the phase offset with regard to the astronomical state at time ''t'' = 0 . There is one term for the Moon and a second term for the Sun. The phase of the first harmonic for the Moon term is called the
lunitidal interval The lunitidal interval measures the time lag from lunar culmination In observational astronomy, culmination is the instant of time of the transit of a astronomical object, celestial object (the Sun, the Moon, a planet, a star, constellation or a ...
or high water interval. The next refinement is to accommodate the harmonic terms due to the elliptical shape of the orbits. To do so, the value of the amplitude is taken to be not a constant, but varying with time, about the average amplitude . To do so, replace in the above equation with where A is another sinusoid, similar to the cycles and epicycles of Ptolemy, Ptolemaic theory. This gives: : $A\left(t\right) = A_o\bigl\left(1 + A_a \cos\,\left(\omega_a t + p_a\right)\bigr\right)$ which is to say an average value with a sinusoidal variation about it of magnitude , with frequency and phase . Substituting this for A_o in the original equation gives a product of two cosine factors: : $A_o \bigl\left( 1 + A_a \cos\,\left(\omega_a t + p_a\right)\bigr\right) \cos\,\left(\omega t + p\right)$ Given that for any and : $\cos x \cos y = \cos\,\left( x + y \right) + \cos\,\left( x - y \right)$ it is clear that a compound term involving the product of two cosine terms each with their own frequency is the same as ''three'' simple cosine terms that are to be added at the original frequency and also at frequencies which are the sum and difference of the two frequencies of the product term. (Three, not two terms, since the whole expression is $\left(1 + \cos x\right)\cos y$.) Consider further that the tidal force on a location depends also on whether the Moon (or the Sun) is above or below the plane of the Equator, and that these attributes have their own periods also incommensurable with a day and a month, and it is clear that many combinations result. With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences to form the frequency of each simple cosine term. Remember that astronomical tides do ''not'' include weather effects. Also, changes to local conditions (sandbank movement, dredging harbour mouths, etc.) away from those prevailing at the measurement time affect the tide's actual timing and magnitude. Organisations quoting a "highest astronomical tide" for some location may exaggerate the figure as a safety factor against analytical uncertainties, distance from the nearest measurement point, changes since the last observation time, ground subsidence, etc., to avert liability should an engineering work be overtopped. Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide from the observed tide. Careful Fourier data analysis over a nineteen-year period (the ''National Tidal Datum Epoch'' in the U.S.) uses frequencies called the ''tidal harmonic constituents''. Nineteen years is preferred because the Earth, Moon and Sun's relative positions repeat almost exactly in the Metonic cycle of 19 years, which is long enough to include the 18.613 year Lunar node, lunar nodal Earth tide#Tidal constituents, tidal constituent. This analysis can be done using only the knowledge of the forcing ''period'', but without detailed understanding of the mathematical derivation, which means that useful tidal tables have been constructed for centuries. The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (the ''semi-diurnal'' constituents), but there are major constituents near 24 hours (''diurnal'') as well. Longer term constituents are 14 day or ''fortnightly'', monthly, and semiannual. Semi-diurnal tides dominated coastline, but some areas such as the South China Sea and the Gulf of Mexico are primarily diurnal. In the semi-diurnal areas, the primary constituents ''M''2 (lunar) and ''S''2 (solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period). In the ''M''2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich. The lines rotate around the
amphidromic point An amphidromic point, also called a tidal node, is a geographical location which has zero tidal for one of the . The (the , or height difference between high tide and low tide) for that harmonic constituent increases with distance from this po ...
s counterclockwise in the northern hemisphere so that from Baja California Peninsula to Alaska and from France to Ireland the ''M''2 tide propagates northward. In the southern hemisphere this direction is clockwise. On the other hand, ''M''2 tide propagates counterclockwise around New Zealand, but this is because the islands act as a dam and permit the tides to have different heights on the islands' opposite sides. (The tides do propagate northward on the east side and southward on the west coast, as predicted by theory.) The exception is at Cook Strait where the tidal currents periodically link high to low water. This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high water across from low water at each end of Cook Strait. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the ''M''2 patterns cannot be used for other tide components.

## Example calculation

Because the Moon is moving in its orbit around the Earth and in the same sense as the Earth's rotation, a point on the Earth must rotate slightly further to catch up so that the time between semi-diurnal tides is not twelve but 12.4206 hours—a bit over twenty-five minutes extra. The two peaks are not equal. The two high tides a day alternate in maximum heights: lower high (just under three feet), higher high (just over three feet), and again lower high. Likewise for the low tides. When the Earth, Moon, and Sun are in line (Sun–Earth–Moon, or Sun–Moon–Earth) the two main influences combine to produce spring tides; when the two forces are opposing each other as when the angle Moon–Earth–Sun is close to ninety degrees, neap tides result. As the Moon moves around its orbit it changes from north of the Equator to south of the Equator. The alternation in high tide heights becomes smaller, until they are the same (at the lunar equinox, the Moon is above the Equator), then redevelop but with the other polarity, waxing to a maximum difference and then waning again.

## Current

The tides' influence on ocean current, current or flow is much more difficult to analyze, and data is much more difficult to collect. A tidal height is a scalar quantity (physics), scalar quantity and varies smoothly over a wide region. A flow is a vector quantity, with magnitude and direction, both of which can vary substantially with depth and over short distances due to local bathymetry. Also, although a water channel's center is the most useful measuring site, mariners object when current-measuring equipment obstructs waterways. A flow proceeding up a curved channel may have similar magnitude, even though its direction varies continuously along the channel. Surprisingly, flood and ebb flows are often not in opposite directions. Flow direction is determined by the upstream channel's shape, not the downstream channel's shape. Likewise, Eddy (fluid dynamics), eddies may form in only one flow direction. Nevertheless, tidal current analysis is similar to tidal heights analysis: in the simple case, at a given location the flood flow is in mostly one direction, and the ebb flow in another direction. Flood velocities are given positive sign, and ebb velocities negative sign. Analysis proceeds as though these are tide heights. In more complex situations, the main ebb and flood flows do not dominate. Instead, the flow direction and magnitude trace an ellipse over a tidal cycle (on a polar plot) instead of along the ebb and flood lines. In this case, analysis might proceed along pairs of directions, with the primary and secondary directions at right angles. An alternative is to treat the tidal flows as complex numbers, as each value has both a magnitude and a direction. Tide flow information is most commonly seen on nautical charts, presented as a table of flow speeds and bearings at hourly intervals, with separate tables for spring and neap tides. The timing is relative to high water at some harbour where the tidal behaviour is similar in pattern, though it may be far away. As with tide height predictions, tide flow predictions based only on astronomical factors do not incorporate weather conditions, which can ''completely'' change the outcome. The tidal flow through Cook Strait between the two main islands of New Zealand is particularly interesting, as the tides on each side of the strait are almost exactly out of phase, so that one side's high water is simultaneous with the other's low water. Strong currents result, with almost zero tidal height change in the strait's center. Yet, although the tidal surge normally flows in one direction for six hours and in the reverse direction for six hours, a particular surge might last eight or ten hours with the reverse surge enfeebled. In especially boisterous weather conditions, the reverse surge might be entirely overcome so that the flow continues in the same direction through three or more surge periods. A further complication for Cook Strait's flow pattern is that the tide at the south side (e.g. at Nelson, New Zealand, Nelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the north side's tidal pattern has only ''one'' cycle per month, as on the east side: Wellington, and Napier, New Zealand, Napier. The graph of Cook Strait's tides shows separately the high water and low water height and time, through November 2007; these are ''not'' measured values but instead are calculated from tidal parameters derived from years-old measurements. Cook Strait's nautical chart offers tidal current information. For instance the January 1979 edition for 41°13·9’S 174°29·6’E (north west of Cape Terawhiti) refers timings to Westport, New Zealand, Westport while the January 2004 issue refers to Wellington. Near Cape Terawhiti in the middle of Cook Strait the tidal height variation is almost nil while the tidal current reaches its maximum, especially near the notorious Karori Rip. Aside from weather effects, the actual currents through Cook Strait are influenced by the tidal height differences between the two ends of the strait and as can be seen, only one of the two spring tides at the north west end of the strait near Nelson has a counterpart spring tide at the south east end (Wellington), so the resulting behaviour follows neither reference harbour.

## Power generation

Tidal energy can be extracted by two means: inserting a water turbine into a tidal current, or building ponds that release/admit water through a turbine. In the first case, the energy amount is entirely determined by the timing and tidal current magnitude. However, the best currents may be unavailable because the turbines would obstruct ships. In the second, the impoundment dams are expensive to construct, natural water cycles are completely disrupted, ship navigation is disrupted. However, with multiple ponds, power can be generated at chosen times. So far, there are few installed systems for tidal power generation (most famously, Rance tidal power plant, La Rance at St Malo, Saint Malo, France) which face many difficulties. Aside from environmental issues, simply withstanding corrosion and biological fouling pose engineering challenges. Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, save for weather effects. While some generation is possible for most of the tidal cycle, in practice turbines lose efficiency at lower operating rates. Since the power available from a flow is proportional to the cube of the flow speed, the times during which high power generation is possible are brief.

Tidal flows are important for navigation, and significant errors in position occur if they are not accommodated. Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant Draft (hull), draft from entering at low tide. Until the advent of automated navigation, competence in calculating tidal effects was important to naval officers. The certificate of examination for lieutenants in the Royal Navy once declared that the prospective officer was able to "shift his tides". Tidal flow timings and velocities appear in ''tide charts'' or a tidal stream atlas. Tide charts come in sets. Each chart covers a single hour between one high water and another (they ignore the leftover 24 minutes) and show the average tidal flow for that hour. An arrow on the tidal chart indicates the direction and the average flow speed (usually in Knot (unit), knots) for spring and neap tides. If a tide chart is not available, most nautical charts have "tidal diamonds" which relate specific points on the chart to a table giving tidal flow direction and speed. The standard procedure to counteract tidal effects on navigation is to (1) calculate a "dead reckoning" position (or DR) from travel distance and direction, (2) mark the chart (with a vertical cross like a plus sign) and (3) draw a line from the DR in the tide's direction. The distance the tide moves the boat along this line is computed by the tidal speed, and this gives an "estimated position" or EP (traditionally marked with a dot in a triangle). Nautical charts display the water's "charted depth" at specific locations with "Echo sounding, soundings" and the use of bathymetric contour lines to depict the submerged surface's shape. These depths are relative to a "chart datum", which is typically the water level at the lowest possible astronomical tide (although other datums are commonly used, especially historically, and tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle. "Drying heights" may also be shown on the chart, which are the heights of the exposed seabed at the lowest astronomical tide. Tide tables list each day's high and low water heights and times. To calculate the actual water depth, add the charted depth to the published tide height. Depth for other times can be derived from tidal curves published for major ports. The rule of twelfths can suffice if an accurate curve is not available. This approximation presumes that the increase in depth in the six hours between low and high water is: first hour — 1/12, second — 2/12, third — 3/12, fourth — 3/12, fifth — 2/12, sixth — 1/12.

# Biological aspects

## Intertidal ecology

Intertidal ecology is the study of ecosystems between the low- and high-water lines along a shore. At low water, the intertidal zone is exposed (or ''emersed''), whereas at high water, it is underwater (or ''immersed''). Intertidal ecologists therefore study the interactions between intertidal organisms and their environment, as well as among the biological interaction, different species. The most important interactions may vary according to the type of intertidal community. The broadest classifications are based on substrates — rocky shore or soft bottom. Intertidal organisms experience a highly variable and often hostile environment, and have adaptation, adapted to cope with and even exploit these conditions. One easily visible feature is vertical zonation, in which the community divides into distinct horizontal bands of specific species at each elevation above low water. A species' ability to cope with desiccation determines its upper limit, while competition (biology), competition with other species sets its lower limit. Humans Exploitation of natural resources, use Intertidal ecology, intertidal regions for food and recreation. Overexploitation can damage intertidals directly. Other anthropogenic actions such as introducing invasive species and global warming, climate change have large negative effects. Marine Protected Areas are one option communities can apply to protect these areas and aid scientific research.

## Biological rhythms

The approximately fortnightly tidal cycle has large effects on intertidal and marine organisms. Hence their biological rhythms tend to occur in rough multiples of this period. Many other animals such as the vertebrates, display similar rhythms. Examples include gestation and egg hatching. In humans, the menstrual cycle lasts roughly a lunar month, an even multiple of the tidal period. Such parallels at least hint at the common descent of all animals from a marine ancestor.

# Other tides

When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internal waves with tidal frequencies. Such waves are called ''internal tides''. Shallow areas in otherwise open water can experience rotary tidal currents, flowing in directions that continually change and thus the flow direction (not the flow) completes a full rotation in hours (for example, the Nantucket Shoals).Le Lacheur, Embert A
Tidal currents in the open sea: Subsurface tidal currents at Nantucket Shoals Light Vessel
''Geographical Review'', April 1924. Accessed: 4 February 2012.
In addition to oceanic tides, large lakes can experience small tides and even planets can experience ''atmospheric tides'' and ''
Earth tide Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...
s''. These are continuum mechanics, continuum mechanical phenomena. The first two take place in fluid mechanics, fluids. The third affects the Earth's thin Solid mechanics, solid crust surrounding its semi-liquid interior (with various modifications).

## Lake tides

Large lakes such as Lake Superior, Superior and Lake Erie, Erie can experience tides of , but these can be masked by meteorologically induced phenomena such as seiche. The tide in Lake Michigan is described as or . This is so small that other larger effects completely mask any tide, and as such these lakes are considered non-tidal.

## Atmospheric tides

Atmospheric tides are negligible at ground level and aviation altitudes, masked by weather's much more important effects. Atmospheric tides are both gravitational and thermal in origin and are the dominant dynamics from about , above which the molecular density becomes too low to support fluid behavior.

## Earth tides

Earth tides or terrestrial tides affect the entire Earth's mass, which acts similarly to a liquid gyroscope with a very thin crust. The Earth's crust shifts (in/out, east/west, north/south) in response to lunar and solar gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, terrestrial tides' semi-diurnal amplitude can reach about at the Equator— due to the Sun—which is important in GPS calibration and VLBI measurements. Precise astronomical angular measurements require knowledge of the Earth's rotation rate and polar motion, both of which are influenced by Earth tides. The semi-diurnal ''M''2 Earth tides are nearly in phase with the Moon with a lag of about two hours.

## Galactic tides

''Galactic tides'' are the tidal forces exerted by galaxies on stars within them and Satellite galaxy, satellite galaxies orbiting them. The galactic tide's effects on the Solar System's Oort cloud are believed to cause 90 percent of long-period comets.

# Misnomers

Tsunamis, the large waves that occur after earthquakes, are sometimes called ''tidal waves'', but this name is given by their ''resemblance'' to the tide, rather than any causal link to the tide. Other phenomena unrelated to tides but using the word ''tide'' are rip current, rip tide, storm tide, hurricane tide, and oil spill, black or red tides. Many of these usages are historic and refer to the earlier meaning of tide as "a portion of time, a season".

* * * * * * * * * * * * * * * * * * * * * * *

# References

150 Years of Tides on the Western Coast: The Longest Series of Tidal Observations in the Americas
NOAA (2004).
Eugene I. Butikov: ''A dynamical picture of the ocean tides''

Why the centrifugal force does not explain the tide's opposite lobe (with nice animations).
O. Toledano ''et al.'' (2008): ''Tides in asynchronous binary systems''
* Gaylord Johnso
"How Moon and Sun Generate the Tides"
''Popular Science'', April 1934 *

NOAA Tides and Currents information and data