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
vorticity", with being "relative vorticity", defined as the vertical component of the curl of the fluidvelocity and "f" is the " Coriolis parameter"
where is the
angular frequencyof the planet'srotation (=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 directionand is the component of velocity in this direction.
In 1950, Charney, Fjorloft, and von Neumann integrated this equation (with an added
diffusionterm on the RHS) on a computerfor the first time, using an observed field of 500 hPa geopotential heightfor the first timestep. This was the one of the first successful instances of numerical weather forecasting.
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