Geophysical fluid dynamics, in its broadest meaning, is the application offluid dynamics to naturally occurring flows, such as lava,oceans, andatmospheres, onEarth and otherplanets.^[1]

Two physical features that are common to many of the phenomena studied in geophysical fluid dynamics arerotation of the fluid due to the planetary rotation andstratification (layering).

The applications of geophysical fluid dynamics do not generally include the circulation of themantle, which is the subject ofgeodynamics, or fluid phenomena in themagnetosphere.Ocean circulation andair circulation are typically studied in oceanography and meteorology.

To describe the flow of geophysical fluids, equations are needed forconservation of momentum (orNewton's second law) andconservation of energy. The former leads to theNavier–Stokes equations 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 beincompressible. Remarkably, this works well even for a highly compressible fluid like air as long assound andshock waves can be ignored.^[2]: 2–3 Second, the fluid is assumed to be aNewtonian fluid, meaning that there is a linear relation between theshear stressτ and thestrainu, for example

${\displaystyle \tau =\mu \frac{du}{dx},}$

whereμ is theviscosity.^[2]: 2–3 Under these assumptions the Navier-Stokes equations are

${\displaystyle \stackrel{\text{Inertia (per volume)}}{\overbrace{\rho (\underset{\begin{array}{c}\text{Eulerian}\\ \text{acceleration}\end{array}}{\underbrace{\frac{\mathrm{\partial }\mathbf{v}}{\mathrm{\partial }t}}}+\underset{\begin{array}{c}\text{Advection}\end{array}}{\underbrace{\mathbf{v}\cdot \mathrm{\nabla }\mathbf{v}}})}}=\stackrel{\text{Divergence of stress}}{\overbrace{\underset{\begin{array}{c}\text{Pressure}\\ \text{gradient}\end{array}}{\underbrace{-\mathrm{\nabla }p}}+\underset{\text{Viscosity}}{\underbrace{\mu {\mathrm{\nabla }}^2\mathbf{v}}}}}+\underset{\begin{array}{c}\text{Other}\\ \text{body}\\ \text{forces}\end{array}}{\underbrace{\mathbf{f}}}.}$

The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (aLagrangian frame of reference). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity andadvection, a measure of the rate of flow in or out of a small region.^{[2]: 44–45}

The equation for energy conservation is essentially an equation for heat flow. If heat is transported byconduction, the heat flow is governed by adiffusion equation. If there are alsobuoyancy effects, for example hot air rising, thennatural convection, also known as free convection, can occur.^[2]: 171 Convection in the Earth'souter core drives thegeodynamo that is the source of theEarth's magnetic field.^{[3]: Chapter 8} In the ocean, convection can bethermal (driven by heat),haline (where the buoyancy is due to differences in salinity), orthermohaline, a combination of the two.^[4]

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 becomestratified. On a large scale, Earth's atmosphere isdivided into a series of layers. Going upwards from the ground, these are thetroposphere,stratosphere,mesosphere,thermosphere, andexosphere.^[5]

The density of air is mainly determined by temperature andwater vapor content, the density ofsea water by temperature andsalinity, 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 apycnocline (density),thermocline (temperature),halocline (salinity), orchemocline (chemistry, including oxygenation).

The same buoyancy that gives rise to stratification also drivesgravity waves. If the gravity waves occur within the fluid, they are calledinternal waves.^{[2]: 208–214}

In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using theBoussinesq approximation. This ignores variations in density except where they are multiplied by thegravitational accelerationg.^[2]: 188

If the pressure depends only on density and vice versa, the fluid dynamics are calledbarotropic. In the atmosphere, this corresponds to a lack of fronts, as in thetropics. If there are fronts, the flow isbaroclinic, and instabilities such ascyclones can occur.^[6]

• Coriolis effect
• Circulation
• Kelvin's circulation theorem
• Vorticity equation
• Thermal wind
• Geostrophic current
• Geostrophic wind
• Taylor–Proudman theorem
• Hydrostatic equilibrium
• Ekman spiral
• Ekman layer

• Atmospheric circulation
• Ocean current
• Ocean dynamics
• Thermohaline circulation
• Boundary current
• Sverdrup balance
• Subsurface currents

• Kelvin wave
• Rossby wave
• Sverdrup wave (Poincaré wave)

• Gravity wave

• Geophysical Fluid Dynamics Laboratory

• Geophysical Fluid Dynamics Program (Woods Hole Oceanographic Institution)
• Geophysical Fluid Dynamics Laboratory (University of Washington)

• Atmospheric dynamics
• Geophysics
• Fluid dynamics
• Physical oceanography

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