By filtering out inertia-gravity oscillations, balance models isolate the slow evolution of a flow. By contrast, primitive equation (PE) models include the fast motions associated with these oscillations. The standard Balance Equations (BE; Charney 1962), which are derived using the horizontal divergence and vertical vorticity equations, are formally valid when the divergence is small. The BE system has become standard for many applications where the divergence is not large. The Asymmetric Balance (AB) formulation (Shapiro and Montgomery 1993), which is derived using the radial and tangential momentum equations for disturbances on a symmetric vortex, is formally valid when the divergence is not necessarily small. The condition for the validity of AB is that the square of the local Rossby number, which is the ratio between the orbital and inertia frequencies, is small. The AB formulation, which was developed to study the evolution of rapidly rotating vortices, has been used in many applications related to tropical cyclone dynamics. Like quasigeostrophic theory, AB has a single prognostic equation for the geopotential.

While in principle the BE system should perform well when the divergence is small, and AB system should perform well when the local Rossby number is small (with the divergence not necessarily small), a quantitative comparison of the accuracy of the BE and AB systems has until now not been made. The simplest model to include divergence is the shallow water model. In the present study simple numerical experiments with such a model are being made to compare the evolution of disturbances using both the BE system and the AB system with that using PE. The equations in each system are linearized on a symmetric vortex in gradient wind balance. Since the system is linear, experiments can be made with single azimuthal-wavenumber disturbances; here we will focus on azimuthal wavenumber two.

Experiments with both free and forced disturbances are being made. In the former case the winds and heights in balance with an azimuthal-wavenumber two PV anomaly are used to initialize both of the balance as well as the primitive equation models. In the latter case an azimuthal-wavenumber two mass source that rotates with the symmetric vortex flow continuously forces a disturbance in wind and height in each of the models. In both types of experiments the evolution of potential vorticity is used to evaluate the accuracy of the BE and AB models versus the PE benchmark. Results of the evaluation will be presented as available.