Accuracy of the linearized standard balance and asymmetric balance systems in a shallow-water numerical model

Abstract

A numerical evaluation of the accuracy of the standard balance equations (BE) and the asymmetric balance equations (AB) in strong vortex applications is presented. Linearized equations for the evolution of disturbances on a symmetric hurricane-like vortex in a shallow-water model are used to compare forecasts using the AB and BE formulations with benchmark primitive equation forecasts. The validity of the BE and AB models is formally determined by the square of the Froude number, F 2 , and the square of the local Rossby number for disturbances with azimuthal wavenumber n, R n 2 , respectively. The numerical experiments demonstrate that accurate results can be achieved with BE and AB in situations where F 2 and R n 2 , respectively, are not necessarily small. When the divergence of the asymmetric disturbance is not much smaller than its vorticity, and the azimuthal wavenumber of the disturbance is low, the AB system proves to be a useful alternative to BE.