Tides are the rise and fall of sea levels caused by the combined
effects of the gravitational forces exerted by the
Contents 1 Characteristics 1.1 Definitions 2 Tidal constituents 2.1 Principal lunar semi-diurnal constituent 2.2 Range variation: springs and neaps 2.3 Lunar altitude 2.4 Other constituents 2.5 Phase and amplitude 3 Physics 3.1 History of tidal physics 3.2 Forces 3.3 Laplace's tidal equations 3.4 Amplitude and cycle time 3.5 Dissipation 3.6 Bathymetry 4 Observation and prediction 4.1 History 4.2 Timing 4.3 Analysis 4.4 Example calculation 4.5 Current 4.6 Power generation 5 Navigation 6 Biological aspects 6.1 Intertidal ecology 6.2 Biological rhythms 7 Other tides 7.1 Lake tides
7.2 Atmospheric tides
7.3
8 Misnomers 9 See also 10 References 11 Further reading 12 External links Characteristics "Ebb tide" redirects here. For other uses, see Ebb tide (other). Types of tides (See Timing (below) for coastal map)
Oscillating currents produced by tides are known as tidal streams. The
moment that the tidal current ceases is called slack water or slack
tide. The tide then reverses direction and is said to be turning.
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 (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.
Illustration by the course of half a month 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
The types of tides Animation of tides as the
Main article: Tidal range
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 and full moon when the
Sun, Moon, and
Spring tide:
Neap tide:
Spring tide:
Neap tide:
Spring tide:
Lunar altitude Low tide at Bangchuidao Scenic Area, Dalian, Liaoning Province, China Low tide at
Low tide at Bar Harbor, Maine, U.S. (2014) The changing distance separating the
The M2 tidal constituent. Amplitude is indicated by color, and the
white lines are cotidal differing by 1 hour. The colors indicate where
tides are most extreme (highest highs, lowest lows), with blues being
least extreme. In almost a dozen places on this map the lines
converge. Notice how at each of these places the surrounding color is
blue, indicating little or no tide. These convergent areas are called
amphidromic points. The curved arcs around the amphidromic points show
the direction of the tides, each indicating a synchronized 6-hour
period. Tidal ranges generally increase with increasing distance from
amphidromic points.
Because the M2 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 of constant
altitude on topographical maps. 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.
The lunar gravity differential field at the Earth's surface is known as the tide-generating force. This is the primary mechanism that drives tidal action and explains two equipotential tidal bulges, accounting for two daily high waters. The ocean's surface is closely approximated by an equipotential
surface, (ignoring ocean currents) commonly referred to as the geoid.
Since the gravitational force is equal to the potential's gradient,
there are no tangential forces on such a surface, and the ocean
surface is thus in gravitational equilibrium. Now consider the effect
of massive external bodies such as the
The vertical (or radial) velocity is negligible, and there is no
vertical shear—this is a sheet flow.
The forcing is only horizontal (tangential).
The
The boundary conditions dictate no flow across the coastline and free
slip at the bottom.
The
The harbour of
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 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 and the time of
high or low tide (the lunitidal interval) 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, U.S., predictably occurs approximately two and a half hours
before the
Brouscon's Almanach of 1546: Compass bearings of high waters in the
Brouscon's Almanach of 1546: Tidal diagrams "according to the age of the moon". From ancient times, tidal observation and discussion has increased in
sophistication, first marking the daily recurrence, then tides'
relationship to the sun and moon.
The same tidal forcing has different results depending on many factors, including coast orientation, continental shelf margin, water body dimensions. The tidal forces due to the
A regular water level chart Isaac Newton'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 over many days. In addition, precise results require detailed knowledge of the shape of all the ocean basins—their bathymetry, and coastline shape. Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by 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
A cos ( ω t + p ) displaystyle Acos ,(omega t+p) where A is the amplitude, ω is the angular frequency usually given in degrees per hour corresponding to t measured in hours, and p 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 p of the first harmonic for the moon term is called the lunitidal interval or high water interval. The next step is to accommodate the harmonic terms due to the elliptical shape of the orbits. Accordingly, the value of A is not a constant but also varying with time, slightly, about some average figure. Replace it then by A(t) where A is another sinusoid, similar to the cycles and epicycles of Ptolemaic theory. Accordingly, A ( t ) = A ( 1 + A a cos ( ω a t + p a ) ) displaystyle A(t)=A bigl ( 1+A_ a cos ,(omega _ a t+p_ a ) bigr ) which is to say an average value A with a sinusoidal variation about it of magnitude Aa, with frequency ωa and phase pa. Thus the simple term is now the product of two cosine factors: A [ 1 + A a cos ( ω a t + p a ) ] cos ( ω t + p ) displaystyle A bigl [ 1+A_ a cos ,(omega _ a t+p_ a ) bigr ] cos ,(omega t+p) Given that for any x and y cos x cos y = 1 2 cos ( x + y ) + 1 2 cos ( x − y ) displaystyle cos xcos y= textstyle frac 1 2 cos ,(x+y)+ textstyle frac 1 2 cos ,(x-y) 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 ( 1 + cos x ) cos y displaystyle (1+cos x)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. Tidal prediction summing constituent parts. 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.
Tides at Bridgeport, Connecticut, U.S.A. during a 50-hour period. Tides at Bridgeport, Connecticut, U.S.A. during a 30-day period. Tides at Bridgeport, Connecticut, U.S.A. during a 400-day period. Tidal patterns in Cook Strait. The north part (Nelson) has two spring
tides per month, versus only one on the south side (
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 semidiurnal
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 current flow is much more difficult to
analyse, and data is much more difficult to collect. A tidal height is
a simple number which applies to a wide region simultaneously. A flow
has both a magnitude and a 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 is the same
flow, 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, eddies may form
in only one flow direction.
Nevertheless, current analysis is similar to tidal 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.
US civil and maritime uses of tidal data 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 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
Tidal Indicator, Delaware River, Delaware c. 1897. At the time shown
in the figure, the tide is 1 1⁄4 feet above mean low water
and is still falling, as indicated by pointing of the arrow. Indicator
is powered by system of pulleys, cables and a float. (Report Of The
Superintendent Of The
Nautical charts display the water's "charted depth" at specific
locations with "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.
A rock, seen at low water, exhibiting typical intertidal zonation. Main article: Intertidal ecology
Further information: Intertidal zone
Nautical portal
Water portal
Aquaculture
Clairaut's theorem
Coastal erosion
Establishment of a port
Head of tide
Hough function
King tide
Lunar Laser Ranging Experiment
Lunar phase
Marine terrace
Mean high water spring
Mean low water spring
Orbit of the Moon
Primitive equations
Tidal island
Tidal limit
Tidal locking
Tidal prism
Tidal reach
Tidal resonance
Tidal river
Tidal triggering
References ^ Reddy, M.P.M. & Affholder, M. (2002). Descriptive physical
oceanography: State of the Art. Taylor and Francis. p. 249.
ISBN 90-5410-706-5. OCLC 223133263.
^ Hubbard, Richard (1893). Boater's Bowditch: The Small Craft American
Practical Navigator. McGraw-Hill Professional. p. 54.
ISBN 0-07-136136-7. OCLC 44059064.
^ Coastal orientation and geometry affects the phase, direction, and
amplitude of amphidromic systems, coastal Kelvin waves as well as
resonant seiches in bays. In estuaries, seasonal river outflows
influence tidal flow.
^ "Tidal lunar day". NOAA. Do not confuse with the astronomical
lunar day on the Moon. A lunar zenith is the Moon's highest point in
the sky.
^ Mellor, George L. (1996). Introduction to physical oceanography.
Springer. p. 169. ISBN 1-56396-210-1.
^
Further reading 150 Years of Tides on the Western Coast: The Longest Series of Tidal
Observations in the Americas
External links Wikiquote has quotations related to: Tides Wikimedia Commons has media related to Tides.
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