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
is the material derivative and
being relative vorticity, defined as the vertical component of the curl of the fluid
velocity and f is the Coriolis parameter
,
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
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.
