A barotropic atmosphere (where density depends only on pressure, with no horizontal density/temperature gradients on pressure surfaces) supports the fundamental conservation law of absolute vorticity: the sum of relative vorticity (ζ) and planetary vorticity (Coriolis parameter, f) is materially conserved following the fluid motion, expressed as D(ζ+f)/Dt = 0.
In barotropic flow, the vorticity equation simplifies (since baroclinic generation terms, which arise from density-pressure gradient misalignment, vanish identically) to the statement that absolute vorticity...
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