A Simplified Scheme to Simulate Asymmetries Due to the Beta Effect in Barotropic Vortices

Abstract

A simplified scheme to generate vortex asymmetries due to the beta effect from an initially symmetric vortex on a beta plane is described. This approach, based on the time integration of the nondivergent barotropic vorticity equation, was developed to generate asymmetric vortex structure for inclusion in the initial conditions for the GFDL Hurricane Model. The simplification is derived from truncation of an azimuthal wavenumber expansion of the vorticity field variables. In order to determine the optimum lowest-order system, the influence of other wavenumbers (specifically 0, 2, and 3) on the asymmetric dipolar (wavenumber 1) structure and the associated vortex drift was investigated by comparing the results of a hierarchy of models differing in truncation level. The model truncated at wavenumber 2 and, including time-dependent symmetric flow, was chosen as the optimum system. Vortex drift tracks computed with this model compare very well with existing numerical model simulations. The models with a time-dependent symmetric flow produced systematically more westward-(less northward-) directed drift with slower speeds for cyclonic vortices than the models with time-independent symmetric flow. The results presented here clearly show the importance of including time-dependent symmetric flow in a simplified barotropic system. Discussion is developed regarding the interactions between the dipolar vortex and the wavenumber 0 and 2 flows. It appears acceptable to truncate the wavenumber expansion at wavenumber 2. The differences between the models with different levels of simplification increase when a larger initial vortex is used.The generation of the asymmetric flow for incorporation into the hurricane model initial conditions involves several aspects of uncertainty not present in idealized cases. A particular problem is the development of overly strong far-field vorticity (i.e., lying much beyond the hurricane region) possibly resulting from inaccuracies in the symmetric wind profile. During the generation of asymmetries, this is suppressed by damping at large radii. Further investigation is needed into the sensitivity of the resulting hurricane drift to the symmetric wind profile and to the integration cutoff time.