Geophysical fluid dynamics, in its broadest meaning, refers to the fluid dynamics of naturally occurring flows, such as lava flows, oceans, and planetary

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. A ...

s, on

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

and other

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 ...

s. Two physical features that are common to many of the phenomena studied in geophysical fluid dynamics are rotation of the fluid due to the planetary rotation and

stratification Stratification may refer to: Mathematics * Stratification (mathematics), any consistent assignment of numbers to predicate symbols * Data stratification in statistics Earth sciences * Stable and unstable stratification * Stratification, or st ...

(layering). The applications of geophysical fluid dynamics do not generally include the circulation of the

mantle A mantle is a piece of clothing, a type of cloak. Several other meanings are derived from that. Mantle may refer to: *Mantle (clothing), a cloak-like garment worn mainly by women as fashionable outerwear **Mantle (vesture), an Eastern Orthodox ve ...

, which is the subject of

geodynamics Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mo ...

, or fluid phenomena in the

magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior d ...

Fundamentals

To describe the flow of geophysical fluids, equations are needed for

conservation of momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

(or

Newton's second law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...

) and

conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means tha ...

. The former leads to the

Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...

which cannot be solved analytically (yet). Therefore, further approximations are generally made in order to be able to solve these equations. First, the fluid is assumed to be

incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An eq ...

. Remarkably, this works well even for a highly compressible fluid like air as long as

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...

and

shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...

s can be ignored. Second, the fluid is assumed to be a

Newtonian fluid A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of chang ...

, meaning that there is a linear relation between the

shear stress Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...

and the

strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...

, for example :

\tau = \mu \frac,

where is the

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 ...

. Under these assumptions the Navier-Stokes equations are :

\overbrace^ =
\overbrace^ +
\underbrace_.

The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (a Lagrangian frame of reference). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity and

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 ...

, a measure of the rate of flow in or out of a small region. The equation for energy conservation is essentially an equation for heat flow. If heat is transported by

conduction Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble, such as an orchestra. * ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of structured free improvisation ...

, the heat flow is governed by a

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 ...

equation. If there are also

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 ...

effects, for example hot air rising, then

natural convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...

, also known as free convection, can occur. Convection in the Earth's

outer core Earth's outer core is a fluid layer about thick, composed of mostly iron and nickel that lies above Earth's solid inner core and below its mantle. The outer core begins approximately beneath Earth's surface at the core-mantle boundary and e ...

drives the

geodynamo In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can ...

that is the source of the

Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magneti ...

. In the ocean, convection can be ''thermal'' (driven by heat), ''haline'' (where the buoyancy is due to differences in salinity), or ''

thermohaline 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 tem ...

'', a combination of the two.

Buoyancy and stratification

Fluid that is less dense than its surroundings tends to rise until it has the same density as its surroundings. If there is not much energy input to the system, it will tend to become

stratified Stratification may refer to: Mathematics * Stratification (mathematics), any consistent assignment of numbers to predicate symbols * Data stratification in statistics Earth sciences * Stable and unstable stratification * Stratification, or st ...

. On a large scale, Earth's atmosphere is divided into a series of layers. Going upwards from the ground, these are the

troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. Fro ...

stratosphere The stratosphere () is the second layer of the atmosphere of the Earth, located above the troposphere and below the mesosphere. The stratosphere is an atmospheric layer composed of stratified temperature layers, with the warm layers of air h ...

mesosphere The mesosphere (; ) is the third layer of the atmosphere, directly above the stratosphere and directly below the thermosphere. In the mesosphere, temperature decreases as altitude increases. This characteristic is used to define its limits: it ...

thermosphere The thermosphere is the layer in the Earth's atmosphere directly above the mesosphere and below the exosphere. Within this layer of the atmosphere, ultraviolet radiation causes photoionization/photodissociation of molecules, creating ions; the ...

, and

exosphere The exosphere ( grc, ἔξω "outside, external, beyond", grc, σφαῖρα "sphere") is a thin, atmosphere-like volume surrounding a planet or natural satellite where molecules are gravitationally bound to that body, but where the densi ...

. The density of air is mainly determined by temperature and

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 ...

content, the density of

sea water Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has approx ...

by temperature and

salinity Salinity () is the saltiness or amount of salt (chemistry), 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 dimensio ...

, and the density of lake water by temperature. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a

pycnocline A pycnocline is the cline or layer where the density gradient () is greatest within a body of water. An ocean current is generated by the forces such as breaking waves, temperature and salinity differences, wind, Coriolis effect, and tides cause ...

(density),

thermocline A thermocline (also known as the thermal layer or the metalimnion in lakes) is a thin but distinct layer in a large body of fluid (e.g. water, as in an ocean or lake; or air, e.g. an atmosphere) in which temperature changes more drastically with ...

(temperature),

halocline In oceanography, a halocline (from Greek ''hals'', ''halos'' 'salt' and ''klinein'' 'to slope') is a cline, a subtype of chemocline caused by a strong, vertical salinity gradient within a body of water. Because salinity (in concert with te ...

(salinity), or

chemocline A chemocline is a type of cline, a layer of fluid with different properties, characterized by a strong, vertical chemistry gradient within a body of water. In bodies of water where chemoclines occur, the cline separates the upper and lower layer ...

(chemistry, including oxygenation). The same buoyancy that gives rise to stratification also drives

gravity wave In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere a ...

s. If the gravity waves occur within the fluid, they are called

internal wave Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in ...

s. In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using the Boussinesq approximation. This ignores variations in density except where they are multiplied by the

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 bodie ...

. If the pressure depends only on density and vice versa, the fluid dynamics are called

barotropic In fluid dynamics, a barotropic fluid is a fluid whose density is a function of pressure only. The barotropic fluid is a useful model of fluid behavior in a wide variety of scientific fields, from meteorology to astrophysics. The density of most ...

. In the atmosphere, this corresponds to a lack of fronts, as in the

tropics The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S. The tropics are also refer ...

. If there are fronts, the flow is

baroclinic In fluid dynamics, the baroclinity (often called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic flow is one in which the densi ...

, and instabilities such as

cyclone In meteorology, a cyclone () is a large air mass that rotates around a strong center of low atmospheric pressure, counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere as viewed from above (opposite to an an ...

s can occur.

Rotation

Coriolis effect 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 ...

* Circulation *

Kelvin's circulation theorem In fluid mechanics, Kelvin's circulation theorem (named after William Thomson, 1st Baron Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, Mathematical physics, mathematical physicist and ...

* Vorticity equation *

Thermal wind The thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere. It is the hypothetical vertical wind shear that would exist if the winds obey geostrophic balance in the ...

* Geostrophic current *

Geostrophic wind In atmospheric science, geostrophic flow () is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. This condition is called '' geostrophic equilibrium'' or ''geostrophic balan ...

Taylor–Proudman theorem In fluid mechanics, the Taylor–Proudman theorem (after Geoffrey Ingram Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity \Omega, the fluid velocity will ...

Hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planeta ...

Ekman spiral The oceanic, wind driven Ekman spiral is the result of a force balance created by a shear stress force, Coriolis force and the water drag. This force balance gives a resulting current of the water different from the winds. In the ocean, there are t ...

Ekman layer The Ekman layer is the layer in a fluid where there is a force balance between pressure gradient force, Coriolis force and turbulent drag. It was first described by Vagn Walfrid Ekman. Ekman layers occur both in the atmosphere and in the ocean ...

General circulation

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 ...

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 conto ...

Ocean dynamics Ocean dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean. Ocean dynamic ...

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 temp ...

Boundary current Boundary currents are ocean currents with dynamics determined by the presence of a coastline, and fall into two distinct categories: western boundary currents and eastern boundary currents. Eastern boundary currents Eastern boundary currents are ...

Sverdrup balance 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 ...

Subsurface currents A subsurface ocean current is an oceanic current that runs beneath surface currents. Examples include the Equatorial Undercurrents of the Pacific, Atlantic, and Indian Oceans, the California Undercurrent, and the Agulhas Undercurrent, the deep t ...

Waves

Barotropic

Kelvin wave A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the ...

Rossby wave Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby. They are observed in the atmospheres an ...

Sverdrup wave A Sverdrup wave (also known as Poincaré wave, or rotational gravity wave Kundu, P. K., and L. M. Cohen. "Fluid mechanics, 638 pp." Academic, Calif (1990).) is a wave in the ocean, or large lakes, which is affected by gravity and Earth's rotation ( ...

(Poincaré wave)

Baroclinic

Gravity wave In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere a ...

References

External links

Geophysical Fluid Dynamics Program
(

Woods Hole Oceanographic Institution The Woods Hole Oceanographic Institution (WHOI, acronym pronounced ) is a private, nonprofit research and higher education facility dedicated to the study of marine science and engineering. Established in 1930 in Woods Hole, Massachusetts, i ...

)
Geophysical Fluid Dynamics Laboratory
(

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seatt ...

) {{physical oceanography Atmospheric dynamics Geophysics Fluid dynamics Physical oceanography