Abstract
An efficient alternative to the customary balance equation solution procedures is described which gives very similar solutions for those cases when the balance equation is elliptic. This alternative invokes some assumptions that are not usually applied to the nonlinear balance equation, but which are justified by comparisons with the standard solutions to the balance equation in both rectangular and spherical geometries. The solution tends toward a flow with zero absolute vorticity as the pressure field tends toward configurations for which the balance equation is non-elliptic. Such non-elliptic pressure fields correspond to force fields with sufficient positive divergence with respect to space to generate flow divergence. In this case a non-divergent balanced solution may not exist, and is physically meaningless if it does exist, but a reasonable divergent balanced solution can be obtained by the proposed technique.
