ON THE SCALAR-VORTICITY AND HORIZONTAL-DIVERGENCE EQUATIONS

Abstract

It is desirable to treat the horizontal divergence as well as the vertical component of vorticity in reasoning about the wind field. One reason for this is that the vorticity is connected with the intensity of disturbances, the divergence with vertical motion and, hence, weather. Both are synoptically important. Another reason is that, together with boundary conditions and in the absence of discontinuities, these two fields are sufficient to determine the wind field. This co-importance makes desirable an equation for the horizontal divergence comparable to the scalar-vorticity equation. Such an equation is derived in the paper. The physical meanings and orders of magnitude of the various terms of the two equations are discussed. Certain terms of the vorticity equation, ordinarily neglected, are shown to be important.