Nonlinear motion of a barotropic vortex in still air and in an environmental zonal flow

This study employs a Vortex Tracking Semispectral (VTSS) model cast in cyli ndrical coordinates that move with the vortex. Variables are represented sp ectrally in azimuth only, so that the model becomes a set of linear equatio ns for each azimuthal wavenumber component, forced by the environmental flo w and coupled by wave-wave interactions that account for all of the nonline arity. The vortex is advected by the surrounding wind and propagates when p otential vorticity (PV) gradients due to the surrounding flow or the beta e ffect 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 t o be slower than the sum of their individual motions. In still air or unifo rm wind on a b plane, the wave energy spectrum falls off rapidly with waven umber. 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 as ymmetric energy narrows because the WN2 asymmetry is forced directly by the environmental deformation. The deformation-induced asymmetry interferes de structively with WN2 due to internal wave-wave interaction. In a cyclonical ly sheared zonal flow, the deformation-induced and nonlinearly induced asym metries interfere constructively, resulting in a broader spectrum. Energy c ascades from WN2 to wavenumbers greater than or equal to2. A reverse cascad e also carries energy to WN1, changing the beta gyres and the motion. Conse quent 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 a symmetries in the middle of the spectrum, similar wave-wave interactions fo rce WN1, leading to a trochoidal vortex track.