ABOUT THE NATURE OF THE GENERALIZED OMEGA-EQUATION

The generalized omega equation (omega equation) for hydrostatic, invis cid, isentropic, Boussinesq flow is interpreted in terms of the change of differential relative vorticity in a fluid parcel. A new formulati on of the omega equation, consistent with this interpretation, is intr oduced. The formulation can be interpreted as the primitive equation ( PE) counterpart of the Q vector formulation of the quasigeostrophic (Q G) omega equation. This interpretation is equivalent to the interpreta tion of the differential horizontal divergence [(-w(z))(z)] equation a s the PE counterpart of the QG differential vorticity equation. The ge neralized equations also show the role that the rate of change of diff erential ageostrophic vorticity and differential divergence play in fo rcing nonquasigeostrophic vertical velocity and nonquasigeostrophic vo rticity, respectively. This is illustrated by a simple application of the theory for the circulation in a tropical cyclone. Finally, the nec essary and sufficient conditions required to obtain the corresponding QG expressions are specified from the generalized equations.