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Barotropic vorticity equation

A simplified form of the vorticity equation for an inviscid, divergence-free flow, the barotropic vorticity equation can simply be stated as

where is the material derivative and

is absolute vorticity, with being relative vorticity, defined as the vertical component of the curl of the fluid velocity and f is the Coriolis parameter


where is the angular frequency of the planet's rotation (=0.7272*10-4 s-1 for the earth) and is latitude.

In terms of relative vorticity, the equation can be rewritten as

where is the variation of the Coriolis parameter with distance in the north-south direction and is the component of velocity in this direction.

In 1950, Charney, Fjorloft, and von Neumann integrated this equation (with an added diffusion term on the RHS) on a computer for the first time, using an observed field of 500 mb geopotential for the first timestep. This was the one of the first successful instances of numerical weather forecasting.

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