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Convection is single or multiphase
fluid flow In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
that occurs spontaneously due to the combined effects of material property
heterogeneity Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, size ...
and body forces on a
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear f ...
, most commonly
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
and
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
(see
buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pr ...
). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft
solids Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural r ...
or
mixtures In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the ...
where particles can flow. Convective flow may be transient (such as when a multiphase
mixture In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the ...
of
oil An oil is any nonpolar chemical substance that is composed primarily of hydrocarbons and is hydrophobic (does not mix with water) & lipophilic (mixes with other oils). Oils are usually flammable and surface active. Most oils are unsatura ...
and water separates) or
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
(see
Convection cell In the field of fluid dynamics, a convection cell is the phenomenon that occurs when density differences exist within a body of liquid or gas. These density differences result in rising and/or falling currents, which are the key characteristics ...
). The convection may be due to
gravitational In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
,
electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions ...
or fictitious body forces. Heat transfer by natural convection plays a role in the structure of
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
, its
oceans The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wor ...
, and its mantle. Discrete convective cells in the atmosphere can be identified by
clouds In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may ...
, with stronger convection resulting in
thunderstorm A thunderstorm, also known as an electrical storm or a lightning storm, is a storm characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere, known as thunder. Relatively weak thunderstorms are so ...
s. Natural convection also plays a role in
stellar physics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the he ...
. Convection is often categorised or described by the main effect causing the convective flow, e.g. Thermal convection. Convection cannot take place in most solids because neither bulk current flows nor significant
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
of matter can take place.
Granular convection Granular convection is a phenomenon where granular material subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid convection. It is sometimes called the Brazil nut effect, when the largest of irregularly sh ...
is a similar phenomenon in
granular material A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose g ...
Advection In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is al ...
is fluid motion created by velocity instead of thermal gradients. Convective heat transfer is the intentional use of convection as a method for
heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conducti ...
.

# History

In the 1830s, in '' The Bridgewater Treatises'', the term ''convection'' is attested in a scientific sense. In treatise VIII by William Prout, in the book on
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties, ...
, it says:
..This motion of heat takes place in three ways, which a common fire-place very well illustrates. If, for instance, we place a thermometer directly before a fire, it soon begins to rise, indicating an increase of temperature. In this case the heat has made its way through the space between the fire and the thermometer, by the process termed ''
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
''. If we place a second thermometer in contact with any part of the grate, and away from the direct influence of the fire, we shall find that this thermometer also denotes an increase of temperature; but here the heat must have travelled through the metal of the grate, by what is termed '' conduction''. Lastly, a third thermometer placed in the chimney, away from the direct influence of the fire, will also indicate a considerable increase of temperature; in this case a portion of the air, passing through and near the fire, has become heated, and has ''carried'' up the chimney the temperature acquired from the fire. There is at present no single term in our language employed to denote this third mode of the propagation of heat; but we venture to propose for that purpose, the term ''convection'', n_footnote:_[Latin''Convectio'',_a_carrying_or_conveying.html" ;"title="atin.html" ;"title="n footnote: [Latin">n footnote: [Latin''Convectio'', a carrying or conveying">atin.html" ;"title="n footnote: [Latin">n footnote: [Latin''Convectio'', a carrying or conveyingwhich not only expresses the leading fact, but also accords very well with the two other terms.
Later, in the same treatise VIII, in the book on meteorology, the concept of convection is also applied to "the process by which heat is communicated through water".

# Terminology

Today, the word ''convection'' has different but related usages in different scientific or engineering contexts or applications. In
fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...
, ''convection'' has a broader sense: it refers to the motion of fluid driven by density (or other property) difference. In
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
, ''convection'' often refers to heat transfer by convection, where the prefixed variant Natural Convection is used to distinguish the fluid mechanics concept of Convection (covered in this article) from convective heat transfer. Some phenomena which result in an effect superficially similar to that of a convective cell may also be (inaccurately) referred to as a form of convection, e.g. thermo-capilliary convection and
Granular convection Granular convection is a phenomenon where granular material subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid convection. It is sometimes called the Brazil nut effect, when the largest of irregularly sh ...
.

# Mechanisms

Convection may happen in
fluids In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
at all scales larger than a few atoms. There are a variety of circumstances in which the forces required for convection arise, leading to different types of convection, described below. In broad terms, convection arises because of
body force In physics, a body force is a force that acts throughout the volume of a body. Springer site - Book 'Solid mechanics'preview paragraph 'Body forces'./ref> Forces due to gravity, electric fields and magnetic fields are examples of body forces. ...
s acting within the fluid, such as gravity.

## Natural convection

Natural convection is a type of flow, of motion of a liquid such as water or a gas such as air, in which the fluid motion is not generated by any external source (like a pump, fan, suction device, etc.) but by some parts of the fluid being heavier than other parts. In most cases this leads to natural circulation, the ability of a fluid in a system to circulate continuously, with gravity and possible changes in heat energy. The driving force for natural convection is gravity. For example if there is a layer of cold dense air on top of hotter less dense air, gravity pulls more strongly on the denser layer on top, so it falls while the hotter less dense air rises to take its place. This creates circulating flow: convection. As it relies on gravity, there is no convection in free-fall (
inertial In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any accelerat ...
) environments, such as that of the orbiting International Space Station. Natural convection can occur when there are hot and cold regions of either air or water, because both water and air become less dense as they are heated. But, for example, in the world's oceans it also occurs due to salt water being heavier than fresh water, so a layer of salt water on top of a layer of fresher water will also cause convection. Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications. In nature, convection cells formed from air raising above sunlight-warmed land or water are a major feature of all weather systems. Convection is also seen in the rising plume of hot air from
fire Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction products. At a certain point in the combustion reaction, called the ignition point, flames are p ...
,
plate tectonics Plate tectonics (from the la, label= Late Latin, tectonicus, from the grc, τεκτονικός, lit=pertaining to building) is the generally accepted scientific theory that considers the Earth's lithosphere to comprise a number of large ...
, oceanic currents (
thermohaline circulation Thermohaline circulation (THC) is a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes. The adjective ''thermohaline'' derives from '' thermo-'' referring to tempe ...
) and sea-wind formation (where upward convection is also modified by
Coriolis force In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
s). In engineering applications, convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins, and solar ponds. A very common industrial application of natural convection is free air cooling without the aid of fans: this can happen on small scales (computer chips) to large scale process equipment. Natural convection will be more likely and more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection or a larger distance through the convecting medium. Natural convection will be less likely and less rapid with more rapid diffusion (thereby diffusing away the thermal gradient that is causing the convection) or a more viscous (sticky) fluid. The onset of natural convection can be determined by the
Rayleigh number In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a ce ...
(Ra). Note that differences in buoyancy within a fluid can arise for reasons other than temperature variations, in which case the fluid motion is called gravitational convection (see below). However, all types of buoyant convection, including natural convection, do not occur in
microgravity The term micro-g environment (also μg, often referred to by the term microgravity) is more or less synonymous with the terms '' weightlessness'' and ''zero-g'', but emphasising that g-forces are never exactly zero—just very small (on the ...
environments. All require the presence of an environment which experiences
g-force The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measur ...
( proper acceleration). The difference of
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
in the fluid is the key driving mechanism. If the differences of density are caused by heat, this force is called as "thermal head" or "thermal driving head." A fluid system designed for natural circulation will have a heat source and a heat sink. Each of these is in contact with some of the fluid in the system, but not all of it. The heat source is positioned lower than the heat sink. Most materials that are fluid at common temperatures expand when they are heated, becoming less
dense Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
. Correspondingly, they become denser when they are cooled. At the heat source of a system of natural circulation, the heated fluid becomes lighter than the fluid surrounding it, and thus rises. At the heat sink, the nearby fluid becomes denser as it cools, and is drawn downward by gravity. Together, these effects create a flow of fluid from the heat source to the heat sink and back again.

## Gravitational or buoyant convection

Gravitational convection is a type of natural convection induced by buoyancy variations resulting from material properties other than temperature. Typically this is caused by a variable composition of the fluid. If the varying property is a concentration gradient, it is known as solutal convection. For example, gravitational convection can be seen in the diffusion of a source of dry salt downward into wet soil due to the buoyancy of fresh water in saline. Variable
salinity Salinity () is the saltiness or amount of salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal to ...
in water and variable water content in air masses are frequent causes of convection in the oceans and atmosphere which do not involve heat, or else involve additional compositional density factors other than the density changes from thermal expansion (see ''
thermohaline circulation Thermohaline circulation (THC) is a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes. The adjective ''thermohaline'' derives from '' thermo-'' referring to tempe ...
''). Similarly, variable composition within the Earth's interior which has not yet achieved maximal stability and minimal energy (in other words, with densest parts deepest) continues to cause a fraction of the convection of fluid rock and molten metal within the Earth's interior (see below). Gravitational convection, like natural thermal convection, also requires a
g-force The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measur ...
environment in order to occur.

## Solid-state convection in ice

Ice convection on Pluto is believed to occur in a soft mixture of nitrogen ice and
carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the si ...
ice. It has also been proposed for
Europa Europa may refer to: Places * Europe * Europa (Roman province), a province within the Diocese of Thrace * Europa (Seville Metro), Seville, Spain; a station on the Seville Metro * Europa City, Paris, France; a planned development * Europa Cli ...
, and other bodies in the outer solar system.

## Thermomagnetic convection

Thermomagnetic convection can occur when an external magnetic field is imposed on a
ferrofluid Ferrofluid is a liquid that is attracted to the poles of a magnet. It is a colloidal liquid made of nanoscale ferromagnetic or ferrimagnetic particles suspended in a carrier fluid (usually an organic solvent or water). Each magnetic parti ...
with varying
magnetic susceptibility In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ...
. In the presence of a temperature gradient this results in a nonuniform magnetic body force, which leads to fluid movement. A ferrofluid is a liquid which becomes strongly magnetized in the presence of a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
.

## Combustion

In a
zero-gravity Weightlessness is the complete or near-complete absence of the sensation of weight. It is also termed zero gravity, zero G-force, or zero-G. Weight is a measurement of the force on an object at rest in a relatively strong gravitational fi ...
environment, there can be no buoyancy forces, and thus no convection possible, so flames in many circumstances without gravity smother in their own waste gases. Thermal expansion and chemical reactions resulting in expansion and contraction gases allows for ventilation of the flame, as waste gases are displaced by cool, fresh, oxygen-rich gas. moves in to take up the low pressure zones created when flame-exhaust water condenses.

# Examples and applications

Systems of natural circulation include tornadoes and other
weather systems 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 cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the t ...
,
ocean current An ocean current is a continuous, directed movement of sea water generated by a number of forces acting upon the water, including wind, the Coriolis effect, breaking waves, cabbeling, and temperature and salinity differences. Depth contours ...
s, and household ventilation. Some solar water heaters use natural circulation. The
Gulf Stream The Gulf Stream, together with its northern extension the North Atlantic Drift, is a warm and swift Atlantic ocean current that originates in the Gulf of Mexico and flows through the Straits of Florida and up the eastern coastline of the Unit ...
circulates as a result of the evaporation of water. In this process, the water increases in salinity and density. In the North Atlantic Ocean, the water becomes so dense that it begins to sink down. Convection occurs on a large scale in
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. ...
s, oceans,
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
ary mantles, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of our sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a
hurricane A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain and squalls. Dep ...
. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can d ...
s, at speeds which may closely approach that of light.

## Demonstration experiments

Thermal convection in liquids can be demonstrated by placing a heat source (e.g. a
Bunsen burner A Bunsen burner, named after Robert Bunsen, is a kind of ambient air gas burner used as laboratory equipment; it produces a single open gas flame, and is used for heating, sterilization, and combustion. The gas can be natural gas (which is m ...
) at the side of a container with a liquid. Adding a dye to the water (such as food colouring) will enable visualisation of the flow. Another common experiment to demonstrate thermal convection in liquids involves submerging open containers of hot and cold liquid coloured with dye into a large container of the same liquid without dye at an intermediate temperature (eg. a jar of hot tap water coloured red, a jar of water chilled in a fridge coloured blue, lowered into a clear tank of water at room temperature). A third approach is to use two identical jars, one filled with hot water dyed one colour, and cold water of another colour. One jar is then temporarily sealed (eg. with a piece of card), inverted and placed on top of the other. When the card is removed, if the jar containing the warmer liquid is placed on top no convection will occur. If the jar containing colder liquid is placed on top, a convection current will form spontaneously. Convection in gases can be demonstrated using a candle in a sealed space with an inlet and exhaust port. The heat from the candle will cause a strong convection current which can be demonstrated with a flow indicator, such as smoke from another candle, being released near the inlet and exhaust areas respectively.

## Convection cells

A convection cell, also known as a
Bénard cell Benard or Bénard is a surname or given name. Notable people with the name include: Surname * Abraham-Joseph Bénard (1750–1822), French actor of the Comédie-Française * Aimé Bénard (1873–1938), Canadian politician * Alexander Benard, A ...
, is a characteristic fluid flow pattern in many convection systems. A rising body of fluid typically loses heat because it encounters a colder surface. In liquid, this occurs because it exchanges heat with colder liquid through direct exchange. In the example of the Earth's atmosphere, this occurs because it radiates heat. Because of this heat loss the fluid becomes denser than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance, its downward force overcomes the rising force beneath it, and the fluid begins to descend. As it descends, it warms again and the cycle repeats itself.

## Atmospheric convection

### Atmospheric circulation

Atmospheric circulation is the large-scale movement of air, and is a means by which
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, d ...
is distributed on the surface of the Earth, together with the much slower (lagged) ocean circulation system. The large-scale structure of the
atmospheric circulation Atmospheric circulation is the large-scale movement of air and together with ocean circulation is the means by which thermal energy is redistributed on the surface of the Earth. The Earth's atmospheric circulation varies from year to year, bu ...
varies from year to year, but the basic climatological structure remains fairly constant. Latitudinal circulation occurs because incident solar
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
per unit area is highest at the heat equator, and decreases as the
latitude In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole ...
increases, reaching minima at the poles. It consists of two primary convection cells, the Hadley cell and the polar vortex, with the Hadley cell experiencing stronger convection due to the release of
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be underst ...
energy by
condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
of
water vapor (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vapor, water vapour or aqueous vapor is the gaseous p ...
at higher altitudes during cloud formation. Longitudinal circulation, on the other hand, comes about because the
ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the worl ...
has a higher specific heat capacity than land (and also
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
, allowing the heat to penetrate further beneath the surface ) and thereby absorbs and releases more
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
, but the temperature changes less than land. This brings the sea breeze, air cooled by the water, ashore in the day, and carries the land breeze, air cooled by contact with the ground, out to sea during the night. Longitudinal circulation consists of two cells, the
Walker circulation The Walker circulation, also known as the Walker cell, is a conceptual model of the air flow in the tropics in the lower atmosphere (troposphere). According to this model, parcels of air follow a closed circulation in the zonal and vertical dir ...
and El Niño / Southern Oscillation.

### Weather

Some more localized phenomena than global atmospheric movement are also due to convection, including wind and some of the hydrologic cycle. For example, a
foehn wind A Foehn or Föhn (, , ), is a type of dry, relatively warm, downslope wind that occurs in the lee (downwind side) of a mountain range. It is a rain shadow wind that results from the subsequent adiabatic warming of air that has dropped most of ...
is a down-slope wind which occurs on the downwind side of a mountain range. It results from the adiabatic warming of air which has dropped most of its moisture on windward slopes. Because of the different adiabatic lapse rates of moist and dry air, the air on the leeward slopes becomes warmer than at the same height on the windward slopes. A
thermal column A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
(or thermal) is a vertical section of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation. The Sun warms the ground, which in turn warms the air directly above it. The warmer air expands, becoming less dense than the surrounding air mass, and creating a
thermal low Thermal lows, or heat lows, are non- frontal low-pressure areas that occur over the continents in the subtropics during the warm season, as the result of intense heating when compared to their surrounding environments.Glossary of Meteorology (20 ...
. The mass of lighter air rises, and as it does, it cools by expansion at lower air pressures. It stops rising when it has cooled to the same temperature as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward moving exterior is caused by colder air being displaced at the top of the thermal. Another convection-driven weather effect is the
sea breeze A sea breeze or onshore breeze is any wind that blows from a large body of water toward or onto a landmass; it develops due to differences in air pressure created by the differing heat capacities of water and dry land. As such, sea breezes a ...
.JetStream: An Online School For Weather (2008)
The Sea Breeze.
National Weather Service The National Weather Service (NWS) is an agency of the United States federal government that is tasked with providing weather forecasts, warnings of hazardous weather, and other weather-related products to organizations and the public for the ...
. Retrieved on 2006-10-24.
Warm air has a lower density than cool air, so warm air rises within cooler air, similar to
hot air balloon A hot air balloon is a lighter-than-air aircraft consisting of a bag, called an envelope, which contains heated air. Suspended beneath is a gondola or wicker basket (in some long-distance or high-altitude balloons, a capsule), which carrie ...
s. Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the
water vapor (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vapor, water vapour or aqueous vapor is the gaseous p ...
in the rising packet of air to
condense Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapo ...
. When the moisture condenses, it releases energy known as
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be underst ...
of condensation which allows the rising packet of air to cool less than its surrounding air, continuing the cloud's ascension. If enough
instability In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be ma ...
is present in the atmosphere, this process will continue long enough for cumulonimbus clouds to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat). All
thunderstorm A thunderstorm, also known as an electrical storm or a lightning storm, is a storm characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere, known as thunder. Relatively weak thunderstorms are so ...
s, regardless of type, go through three stages: the developing stage, the mature stage, and the dissipation stage. The average thunderstorm has a diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through.

## Oceanic circulation

Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the
pole Pole may refer to: Astronomy * Celestial pole, the projection of the planet Earth's axis of rotation onto the celestial sphere; also applies to the axis of rotation of other planets * Pole star, a visible star that is approximately aligned with t ...
s, while cold polar water heads towards the Equator. The surface currents are initially dictated by surface wind conditions. The
trade winds The trade winds or easterlies are the permanent east-to-west prevailing winds that flow in the Earth's equatorial region. The trade winds blow mainly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisph ...
blow westward in the tropics, and the
westerlies The westerlies, anti-trades, or prevailing westerlies, are prevailing winds from the west toward the east in the middle latitudes between 30 and 60 degrees latitude. They originate from the high-pressure areas in the horse latitudes and tren ...
blow eastward at mid-latitudes. This wind pattern applies a stress to the subtropical ocean surface with negative
curl cURL (pronounced like "curl", UK: , US: ) is a computer software project providing a library (libcurl) and command-line tool (curl) for transferring data using various network protocols. The name stands for "Client URL". History cURL was f ...
across the
Northern Hemisphere The Northern Hemisphere is the half of Earth that is north of the Equator. For other planets in the Solar System, north is defined as being in the same celestial hemisphere relative to the invariable plane of the solar system as Earth's North ...
, and the reverse across the Southern Hemisphere. The resulting
Sverdrup transport The Sverdrup balance, or Sverdrup relation, is a theoretical relationship between the wind stress exerted on the surface of the open ocean and the vertically integrated meridional (north-south) transport of ocean water. History Aside from the ...
is equatorward. Because of conservation of
potential vorticity In fluid mechanics, potential vorticity (PV) is a quantity which is proportional to the dot product of vorticity and stratification. This quantity, following a parcel of air or water, can only be changed by diabatic or frictional processes. It ...
caused by the poleward-moving winds on the
subtropical ridge The horse latitudes are the latitudes about 30 degrees north and south of the Equator. They are characterized by sunny skies, calm winds, and very little precipitation. They are also known as subtropical ridges, or highs. It is a high-press ...
's western periphery and the increased relative vorticity of poleward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the cold western boundary current which originates from high latitudes. The overall process, known as western intensification, causes currents on the western boundary of an ocean basin to be stronger than those on the eastern boundary. As it travels poleward, warm water transported by strong warm water current undergoes evaporative cooling. The cooling is wind driven: wind moving over water cools the water and also causes
evaporation Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. High concentration of the evaporating substance in the surrounding gas significantly slows down evaporation, such as when humidi ...
, leaving a saltier brine. In this process, the water becomes saltier and denser. and decreases in temperature. Once sea ice forms, salts are left out of the ice, a process known as brine exclusion. These two processes produce water that is denser and colder. The water across the northern Atlantic ocean becomes so dense that it begins to sink down through less salty and less dense water. (This open ocean convection is not unlike that of a lava lamp.) This downdraft of heavy, cold and dense water becomes a part of the
North Atlantic Deep Water North Atlantic Deep Water (NADW) is a deep water mass formed in the North Atlantic Ocean. Thermohaline circulation (properly described as meridional overturning circulation) of the world's oceans involves the flow of warm surface waters from the ...
, a southgoing stream.

## Mantle convection

Mantle convection is the slow creeping motion of Earth's rocky mantle caused by convection currents carrying heat from the interior of the earth to the surface. It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface. The Earth's surface is divided into a number of
tectonic Tectonics (; ) are the processes that control the structure and properties of the Earth's crust and its evolution through time. These include the processes of mountain building, the growth and behavior of the strong, old cores of continents ...
plates that are continuously being created and consumed at their opposite plate boundaries. Creation (
accretion Accretion may refer to: Science * Accretion (astrophysics), the formation of planets and other bodies by collection of material through gravity * Accretion (meteorology), the process by which water vapor in clouds forms water droplets around nuc ...
) occurs as mantle is added to the growing edges of a plate. This hot added material cools down by conduction and convection of heat. At the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of subduction at an ocean trench. This subducted material sinks to some depth in the Earth's interior where it is prohibited from sinking further. The subducted oceanic crust triggers volcanism. Convection within
Earth's mantle Earth's mantle is a layer of silicate rock between the crust and the outer core. It has a mass of 4.01 × 1024 kg and thus makes up 67% of the mass of Earth. It has a thickness of making up about 84% of Earth's volume. It is predominantly sol ...
is the driving force for
plate tectonics Plate tectonics (from the la, label= Late Latin, tectonicus, from the grc, τεκτονικός, lit=pertaining to building) is the generally accepted scientific theory that considers the Earth's lithosphere to comprise a number of large ...
. Mantle convection is the result of a thermal gradient: the lower mantle is hotter than the upper mantle, and is therefore less dense. This sets up two primary types of instabilities. In the first type, plumes rise from the lower mantle, and corresponding unstable regions of
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
drip back into the mantle. In the second type, subducting oceanic plates (which largely constitute the upper thermal boundary layer of the mantle) plunge back into the mantle and move downwards towards the core-mantle boundary. Mantle convection occurs at rates of centimeters per year, and it takes on the order of hundreds of millions of years to complete a cycle of convection. Neutrino flux measurements from the Earth's core (see
kamLAND The Kamioka Liquid Scintillator Antineutrino Detector (KamLAND) is an electron antineutrino detector at the Kamioka Observatory, an underground neutrino detection facility in Hida, Gifu, Japan. The device is situated in a drift mine shaft in ...
) show the source of about two-thirds of the heat in the inner core is the radioactive decay of 40K, uranium and thorium. This has allowed plate tectonics on Earth to continue far longer than it would have if it were simply driven by heat left over from Earth's formation; or with heat produced from
gravitational potential energy Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conv ...
, as a result of physical rearrangement of denser portions of the Earth's interior toward the center of the planet (i.e., a type of prolonged falling and settling).

## Stack effect

The Stack effect or chimney effect is the movement of air into and out of buildings, chimneys, flue gas stacks, or other containers due to buoyancy. Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The greater the thermal difference and the height of the structure, the greater the buoyancy force, and thus the stack effect. The stack effect helps drive natural ventilation and infiltration. Some
cooling tower A cooling tower is a device that rejects waste heat to the atmosphere through the cooling of a coolant stream, usually a water stream to a lower temperature. Cooling towers may either use the evaporation of water to remove process heat and ...
s operate on this principle; similarly the solar updraft tower is a proposed device to generate electricity based on the stack effect.

## Stellar physics

The convection zone of a star is the range of radii in which energy is transported primarily by convection. Granules on the
photosphere The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/''phos, photos'' meaning "light" and σφαῖρα/''sphaira'' meaning "sphere", in reference to it ...
of the Sun are the visible tops of convection cells in the photosphere, caused by convection of plasma in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours.

## Water convection at freezing temperatures

Water is a fluid that does not obey the Boussinesq approximation. This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures. The density of water reaches a maximum at 4 °C and decreases as the temperature deviates. This phenomenon is investigated by experiment and numerical methods. Water is initially stagnant at 10 °C within a square cavity. It is differentially heated between the two vertical walls, where the left and right walls are held at 10 °C and 0 °C, respectively. The density anomaly manifests in its flow pattern. As the water is cooled at the right wall, the density increases, which accelerates the flow downward. As the flow develops and the water cools further, the decrease in density causes a recirculation current at the bottom right corner of the cavity. Another case of this phenomenon is the event of super-cooling, where the water is cooled to below freezing temperatures but does not immediately begin to freeze. Under the same conditions as before, the flow is developed. Afterward, the temperature of the right wall is decreased to −10 °C. This causes the water at that wall to become supercooled, create a counter-clockwise flow, and initially overpower the warm current. This plume is caused by a delay in the nucleation of the ice. Once ice begins to form, the flow returns to a similar pattern as before and the solidification propagates gradually until the flow is redeveloped.

## Nuclear reactors

In a nuclear reactor, natural circulation can be a design criterion. It is achieved by reducing turbulence and friction in the fluid flow (that is, minimizing
head loss Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum., 410 pages. See pp. 43–44., 650 pages. See p. 22. It is usually measured as a liquid surface elevation, expressed in units of length, ...
), and by providing a way to remove any inoperative pumps from the fluid path. Also, the reactor (as the heat source) must be physically lower than the steam generators or turbines (the heat sink). In this way, natural circulation will ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps. Notable examples are the S5G and
S8G The S8G reactor is a naval reactor used by the United States Navy to provide electricity generation and propulsion on warships. The S8G designation stands for: * S = Submarine platform * 8 = Eighth generation core designed by the contractor * G ...
United States Naval reactor United States naval reactors are nuclear reactors used by the United States Navy aboard certain ships to generate the steam used to produce power for propulsion, electric power, catapulting airplanes in aircraft carriers, and a few more minor ...
s, which were designed to operate at a significant fraction of full power under natural circulation, quieting those propulsion plants. The S6G reactor cannot operate at power under natural circulation, but can use it to maintain emergency cooling while shut down. By the nature of natural circulation, fluids do not typically move very fast, but this is not necessarily bad, as high flow rates are not essential to safe and effective reactor operation. In modern design nuclear reactors, flow reversal is almost impossible. All nuclear reactors, even ones designed to primarily use natural circulation as the main method of fluid circulation, have pumps that can circulate the fluid in the case that natural circulation is not sufficient.

# Mathematical models of convection

A number of dimensionless terms have been derived to describe and predict convection, including the
Archimedes number In viscous fluid dynamics, the Archimedes number (Ar), is a dimensionless number used to determine the motion of fluids due to density differences, named after the ancient Greek scientist and mathematician Archimedes. It is the ratio of gravitati ...
, Grashof number, Richardson number, and the
Rayleigh number In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a ce ...
. In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system. The relative magnitudes of the Grashof number and the square of the
Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be d ...
determine which form of convection dominates. If $\rm Gr/Re^2 \gg 1$, forced convection may be neglected, whereas if $\rm Gr/Re^2 \ll 1$, natural convection may be neglected. If the ratio, known as the Richardson number, is approximately one, then both forced and natural convection need to be taken into account.

## Onset

The onset of natural convection is determined by the
Rayleigh number In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a ce ...
(Ra). This
dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or ...
is given by :$\textbf = \frac$ where *$\Delta \rho$ is the difference in density between the two parcels of material that are mixing *$g$ is the local
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodi ...
*$L$ is the characteristic length-scale of convection: the depth of the boiling pot, for example *$D$ is the
diffusivity Diffusivity is a rate of diffusion, a measure of the rate at which particles or heat or fluids can spread. It is measured differently for different mediums. Diffusivity may refer to: *Thermal diffusivity, diffusivity of heat *Diffusivity of mass: ...
of the characteristic that is causing the convection, and *$\mu$ is the
dynamic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...
. Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid. For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by: :$\Delta\rho=\rho_0 \beta \Delta T$ where *$\rho_0$ is the reference density, typically picked to be the average density of the medium, *$\beta$ is the coefficient of thermal expansion, and *$\Delta T$ is the temperature difference across the medium. The general diffusivity, $D$, is redefined as a
thermal diffusivity In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI ...
, $\alpha$. :$D=\alpha$ Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection. :$\textbf = \frac$

## Turbulence

The tendency of a particular naturally convective system towards turbulence relies on the Grashof number (Gr). :$Gr= \frac$ In very sticky, viscous fluids (large ''ν''), fluid motion is restricted, and natural convection will be non-turbulent. Following the treatment of the previous subsection, the typical fluid velocity is of the order of $g \Delta \rho L^2 / \mu$, up to a numerical factor depending on the geometry of the system. Therefore, Grashof number can be thought of as
Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be d ...
with the velocity of natural convection replacing the velocity in Reynolds number's formula. However In practice, when referring to the Reynolds number, it is understood that one is considering forced convection, and the velocity is taken as the velocity dictated by external constraints (see below).

## Behavior

The Grashof number can be formulated for natural convection occurring due to a concentration gradient, sometimes termed thermo-solutal convection. In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then: :$Gr= \frac$ Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient. A general correlation that applies for a variety of geometries is : The value of f4(Pr) is calculated using the following formula : Nu is the
Nusselt number In thermal fluid dynamics, the Nusselt number (, after Wilhelm Nusselt) is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection (fluid motion) and diffusion (conduction). The conduc ...
and the values of Nu0 and the characteristic length used to calculate Ra are listed below (see also Discussion): Warning: The values indicated for the Horizontal cylinder are wrong; see discussion.

# Natural convection from a vertical plate

One example of natural convection is heat transfer from an isothermal vertical plate immersed in a fluid, causing the fluid to move parallel to the plate. This will occur in any system wherein the density of the moving fluid varies with position. These phenomena will only be of significance when the moving fluid is minimally affected by forced convection. When considering the flow of fluid is a result of heating, the following correlations can be used, assuming the fluid is an ideal diatomic, has adjacent to a vertical plate at constant temperature and the flow of the fluid is completely laminar. Num = 0.478(Gr0.25) Mean
Nusselt number In thermal fluid dynamics, the Nusselt number (, after Wilhelm Nusselt) is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection (fluid motion) and diffusion (conduction). The conduc ...
= Num = hmL/k where *hm = mean coefficient applicable between the lower edge of the plate and any point in a distance L (W/m2. K) *L = height of the vertical surface (m) *k = thermal conductivity (W/m. K) Grashof number = Gr = where *g = gravitational acceleration (m/s2) *L = distance above the lower edge (m) *ts = temperature of the wall (K) *t∞ = fluid temperature outside the thermal boundary layer (K) *v = kinematic viscosity of the fluid (m²/s) *T = absolute temperature (K) When the flow is turbulent different correlations involving the Rayleigh Number (a function of both the Grashof number and the
Prandtl number The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as: : \mathrm = \frac = \fr ...
) must be used. Note that the above equation differs from the usual expression for Grashof number because the value $\beta$ has been replaced by its approximation $1/T$, which applies for ideal gases only (a reasonable approximation for air at ambient pressure).

# Pattern formation

Convection, especially Rayleigh–Bénard convection, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a pattern-forming system. When heat is fed into the system from one direction (usually below), at small values it merely diffuses (''conducts'') from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the
Rayleigh number In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a ce ...
, the system undergoes a
bifurcation Bifurcation or bifurcated may refer to: Science and technology * Bifurcation theory, the study of sudden changes in dynamical systems ** Bifurcation, of an incompressible flow, modeled by squeeze mapping the fluid flow * River bifurcation, the for ...
from the stable ''conducting'' state to the ''convecting'' state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the same volume of fluid rising as falling. This is known as Boussinesq convection. As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
, which may begin to significantly vary horizontally across layers of fluid. This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a
convection cell In the field of fluid dynamics, a convection cell is the phenomenon that occurs when density differences exist within a body of liquid or gas. These density differences result in rising and/or falling currents, which are the key characteristics ...
. As the
Rayleigh number In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a ce ...
is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as spirals, may begin to appear.