Geophysical fluid dynamics, in its broadest meaning, is the application of fluid dynamics to naturally occurring flows, such as lava, oceans, and atmospheres, on Earth and other planets. 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, or fluid phenomena in the magnetosphere. 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 (or Newton's second law) and conservation of energy. The former leads to the Navier–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 be incompressible. Remarkably, this works well even for a highly compressible fluid like air as long as sound and shock waves can be ignored. Second, the fluid is assumed to be a Newtonian fluid, meaning that there is a linear relation between the shear stress τ and the strain u, for example
τ = μ d u d x , {\displaystyle \tau =\mu {\frac {du}{dx}},}
where μ is the viscosity. Under these assumptions the Navier-Stokes equations are
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