Semibalance Model—Connection between Geostrophic-Type and Balanced-Type Intermediate Models

Abstract

A hybrid intermediate model, called the semibalance model, is derived from a single truncation of the vector vorticity equation with a balanced vorticity approximation that neglects the advection and stretching?tilting of the unbalanced secondary flow vorticity. This approximation applies not only to straight fronts, like the semi-geostrophy (SG), but also to highly curved fronts and vortices in which the balanced leading-order velocity and unbalanced secondary vorticity are nearly parallel with slow spatial variations along the front or vortex flow. The semibalance model is similar to the balance equations based on momentum equations (BEM) except that the leading-order flow is nonlinearly balanced and the secondary circulation is not free of vertical vorticity. As in BEM, the truncated potential vorticity in the semibalance model is more accurate than in SG, and the problem with spurious high-frequency oscillation in BEM is eliminated in the semibalance model. The potential vorticity in the semibalance model is not only conserved but also ?invertible,? so the semibalance dynamics can be examined through ?potential vorticity thinking.? In this sense, the semibalance model combines the advantages of SG and BEM. Diagnostic equations for the secondary circulation are derived. The associated boundary value problem is shown to be well posed in iterative form, provided the leading-order potential vorticity is positive and, thus, the flow is inertially and convectively stable. Methods for the numerical solution of the semibalance model are presented. Under more restrictive conditions, the semibalance model reduces to the quasi-balance and bilinear quasi-balance models. Through the semibalance and quasi-balance models, the geostrophic-type and balanced-type models are connected.