About the Nature of the Generalized Omega Equation

Abstract

The generalized omega equation (? equation) for hydrostatic, inviscid, isentropic, Boussinesq flow is interpreted in terms of the change of differential relative vorticity in a fluid parcel. A new formulation of the ? equation, consistent with this interpretation, is introduced. The formulation can be interpreted as the primitive equation (PE) counterpart of the Q vector formulation of the quasigeostrophic (QG) ? equation. This interpretation is equivalent to the interpretation of the differential horizontal divergence [(?wz)z] equation as the PE counterpart of the QG differential vorticity equation. The generalized equations also show the role that the rate of change of differential ageostrophic vorticity and differential divergence play in forcing nonquasigeostrophic vertical velocity and nonquasigeostrophic vorticity, respectively. This is illustrated by a simple application of the theory for the circulation in a tropical cyclone. Finally, the necessary and sufficient conditions required to obtain the corresponding QG expressions are specified from the generalized equations.