# 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.