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