= Geophysical fluid dynamics
{title2=GFD}
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<Geophysical fluid dynamics> studies <fluid flow> on rotating, stratified planets, including <oceans>, <atmospheres> and planetary interiors. The competition among <rotation>, <buoyancy>, <pressure gradients> and <inertia> organizes its useful approximations.
For speed $U$, horizontal <length> $L$ and nonzero <Coriolis parameter> $f$, the <Rossby number>
$$
\mathrm{Ro}=\frac{U}{|f|L}
$$
compares advective <acceleration> $U^2/L$ with <Coriolis acceleration> $|f|U$. Small $\mathrm{Ro}$ motivates <geostrophic balance> between horizontal <pressure gradients> and <Coriolis force>, provided rapid transients and other leading forces are absent. <Stratification> introduces a <buoyancy frequency>, while vertical <hydrostatic balance> can be appropriate when vertical <acceleration> is small.
A rotating-tank experiment makes these balances visible. In the MIT balanced-vortex apparatus, <water> spirals toward a drain; a camera rotating with the tank measures motion relative to it. The <free surface> slope supplies a <pressure gradient>. Comparing relative speed, tank <rotation> and surface slope tests the balance and its <Rossby number> correction. <Balanced Vortex: Theory by Massachusetts Institute of Technology>[Tank experiment, equations 1–6; Atmosphere example, equations 7–11]{ref}
This shared mathematics connects laboratory <rotating fluids> to planetary circulation without assuming that every atmospheric vortex is geostrophic.
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