Nonlinear Motion of a Barotropic Vortex in Still Air and in an Environmental Zonal Flow

Abstract

This study employs a Vortex Tracking Semispectral (VTSS) model cast in cylindrical coordinates that move with the vortex. Variables are represented spectrally in azimuth only, so that the model becomes a set of linear equations for each azimuthal wavenumber component, forced by the environmental flow and coupled by wave?wave interactions that account for all of the nonlinearity. The vortex is advected by the surrounding wind and propagates when potential vorticity (PV) gradients due to the surrounding flow or the ? effect force wavenumber one (WN1) asymmetries. Nonlinearity generally plays a dissipative role. Although propagation is faster in stronger PV gradients, nonlinear interactions cause the motions due to superposed PV gradients to be slower than the sum of their individual motions. In still air or uniform wind on a ? plane, the wave energy spectrum falls off rapidly with wavenumber. For most situations, the calculations converge for truncation at WN6 on a 4000-km domain. In an anticyclonically sheared environmental zonal flow, the spectrum of asymmetric energy narrows because the WN2 asymmetry is forced directly by the environmental deformation. The deformation-induced asymmetry interferes destructively with WN2 due to internal wave?wave interaction. In a cyclonically sheared zonal flow, the deformation-induced and nonlinearly induced asymmetries interfere constructively, resulting in a broader spectrum. Energy cascades from WN2 to wavenumbers ≥2. A reverse cascade also carries energy to WN1, changing the ? gyres and the motion. Consequent perturbation of WN1 leads to slow convergence of the predicted vortex position after 10 simulated days with increasing spectral resolution. When imposed mass sources and sinks are used to supply energy directly to the asymmetries in the middle of the spectrum, similar wave?wave interactions force WN1, leading to a trochoidal vortex track.