The omega equation is of great importance in meteorology and atmospheric physics. It is a partial differential equation for the vertical velocity, which is defined as a Lagrangian rate of change of pressure with time, that is, .
The equation reads:
-
(1)
where is the Coriolis parameter, is the static stability, is the geostrophic velocity vector, is the geostrophic relative vorticity, is the geopotential, is the horizontal Laplacian operator and is the horizontal del operator.
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