Geophysical fluid dynamics, in its broadest meaning, is the application of

fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

to naturally occurring flows, such as lava,

ocean The ocean is the body of salt water that covers approximately 70.8% of Earth. The ocean is conventionally divided into large bodies of water, which are also referred to as ''oceans'' (the Pacific, Atlantic, Indian Ocean, Indian, Southern Ocean ...

s, and

atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...

s, on

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

and other

planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...

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

'', 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 Dynamo ...

. Ocean circulation and air circulation are typically studied in oceanography and meteorology.

Fundamentals

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

conservation of momentum In Newtonian mechanics, momentum (: momenta or momentums; 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. ...

(or Newton's second law) and

conservation of energy The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...

. The former leads to the

Navier–Stokes equations The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Georg ...

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. 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 the br ...

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 cha ...

, meaning that there is a linear relation between the

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

and the strain , for example :

\tau = \mu \frac,

where is the

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

. 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 fields 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 a ...

, 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, 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 p ...

equation. If there are also

buoyancy Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). In a column of fluid, pressure increases with depth as a result of the weight of t ...

effects, for example hot air rising, then

natural convection Convection is single or multiphase fluid flow that occurs spontaneously through 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 conve ...

, also known as free convection, can occur. Convection in the Earth's outer core drives the geodynamo 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 structure of Earth, Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from ...

. In the ocean, convection can be ''thermal'' (driven by heat), ''haline'' (where the buoyancy is due to differences in salinity), or '' thermohaline'', 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. 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 lowest layer of the atmosphere of Earth. It contains 80% of the total mass of the Atmosphere, planetary atmosphere and 99% of the total mass of water vapor and aerosols, and is where most weather phenomena occur. From the ...

stratosphere The stratosphere () is the second-lowest layer of the atmosphere of Earth, located above the troposphere and below the mesosphere. The stratosphere is composed of stratified temperature zones, with the warmer layers of air located higher ...

, mesosphere, thermosphere, and

exosphere The exosphere is a thin, atmosphere-like volume surrounding a planet or natural satellite where molecules are gravitationally bound to that body, but where the density is so low that the molecules are essentially collision-less. In the case of ...

. The density of air is mainly determined by temperature and

water vapor Water vapor, water vapour, or aqueous vapor is the gaseous phase of Properties of water, water. It is one Phase (matter), state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from th ...

content, the density of sea water 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 (density), thermocline (temperature), halocline (salinity), or chemocline (chemistry, including oxygenation). The same buoyancy that gives rise to stratification also drives gravity waves. If the gravity waves occur within the fluid, they are called internal waves. 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 (physics), drag). This is the steady gain in speed caused exclusively by gravitational attraction. All bodi ...

. If the pressure depends only on density and vice versa, the fluid dynamics are called barotropic. In the atmosphere, this corresponds to a lack of fronts, as in the

tropics The tropics are the regions of Earth surrounding the equator, where the sun may shine directly overhead. This contrasts with the temperate or polar regions of Earth, where the Sun can never be directly overhead. This is because of Earth's ax ...

. If there are fronts, the flow is baroclinic, 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 ant ...

s can occur.

Rotation

Coriolis effect In physics, the Coriolis force is a pseudo 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 left of the moti ...

* Circulation * Kelvin's circulation theorem *

Vorticity equation The vorticity equation of fluid dynamics describes the evolution of the vorticity of a particle of a fluid dynamics, fluid as it moves with its flow (fluid), flow; that is, the local rotation of the fluid (in terms of vector calculus this is the ...

* Thermal wind * Geostrophic current * Geostrophic wind * Taylor–Proudman theorem *

Hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and 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. I ...

* Ekman spiral *

Ekman layer Ekman transport is part of Ekman motion theory, first investigated in 1902 by Vagn Walfrid Ekman. Winds are the main source of energy for ocean circulation, and Ekman transport is a component of wind-driven ocean current. Ekman transport occurs ...

General circulation

Atmospheric circulation Atmospheric circulation is the large-scale movement of Atmosphere of Earth, 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 fro ...

Ocean current An ocean current is a continuous, directed movement of seawater 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, sh ...

* Ocean dynamics *

Thermohaline circulation Thermohaline circulation (THC) is a part of the large-scale Ocean current, ocean circulation driven by global density gradients formed by surface heat and freshwater fluxes. The name ''thermohaline'' is derived from ''wikt:thermo-, thermo-'', r ...

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 * Subsurface currents

Waves

Barotropic

Kelvin wave A Kelvin wave is a wave in the ocean, a large lake or the 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-d ...

* Rossby wave * Sverdrup wave (Poincaré wave)

Baroclinic

Gravity wave In fluid dynamics, gravity waves are waves 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 and the oc ...

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, it i ...

)
Geophysical Fluid Dynamics Laboratory
(

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

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