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

<math>\frac{d \eta}{d t} = 0</math>,

where

<math>\eta = \zeta + f</math>

is absolute vorticity, with <math>\zeta</math> being relative vorticity and f the Coriolis parameter[?]

<math>f = 2 \Omega \sin \phi</math>,

where <math>\Omega</math> is the angular frequency and <math>\phi</math> is latitude.

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

<math>\frac{d \zeta}{d t} = -v \beta</math>,

where <math>\beta = \partial f / \partial y</math> is the variation of the Coriolis parameter with latitude.

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[?].

External links:

• http://www.met.rdg.ac.uk/~ross/BarVor.html