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.
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