In this type of atmosphere, high and low pressure areas are centers of warm and cold temperature anomalies.
[1] A simplified form of the vorticity equation for an inviscid, divergence-free flow (solenoidal velocity field), the barotropic vorticity equation can simply be stated as[2] where D/Dt is the material derivative and is absolute vorticity, with ζ being relative vorticity, defined as the vertical component of the curl of the fluid velocity and f is the Coriolis parameter where Ω is the angular frequency of the planet's rotation (Ω = 0.7272×10−4 s−1 for the earth) and φ is latitude.
In terms of relative vorticity, the equation can be rewritten as where β = ∂f/∂y is the variation of the Coriolis parameter with distance y in the north–south direction and v is the component of velocity in this direction.
In 1950, Charney, Fjørtoft, and von Neumann integrated this equation (with an added diffusion term on the right-hand side) on a computer for the first time, using an observed field of 500 hPa geopotential height for the first timestep.
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