Vortex axisymmetrization: Dependence on azimuthal wave-number or asymmetric radial structure changes

Intense vortices in the atmosphere and ocean exhibit a high degree of axisymmetry despite persistent asymmetric forcing from their environment. To further elucidate vortex axisymmetrization a variety of idealized initial-value models for barotropic non-divergent flow is considered. To ensure basic understanding, disturbance evolution is first examined in a rectilinear system of simple shear. Particular emphasis is placed on identifying how inviscid disturbance-evolution depends on the zonal wave-number and on the meridional structure of the initial conditions. Insight acquired from the rectilinear problem is then applied to a bounded Rankine vortex. Here, the dependency of disturbance evolution on the azimuthal wave-number is of special interest. Recent development of a low-frequency balance theory for rapidly rotating (large Rossby number) vortices has provided observational evidence that the low-azimuthal-wave-number asymmetries, especially wave number one, are dominant in the nearvortex region. The results of this work provide further theoretical evidence of an inviscid wave-number-selection mechanism that preferentially damps the high-wave-number asymmetries. The radial structure and location of the initial conditions are found to be important factors in determining how rapidly a disturbance is compressed or elongated. This in turn controls the rate of disturbance growth or decay. For swirling flows, a definition of an effective shear is proposed that accounts for both the radial variations of the initial condition and the radial variation of the angular velocity. Using the reciprocal of this effective shear, time-scales for il disturbance to decay to half its initial energy, the half-life, are calculated for initial conditions and symmetric wind-profiles that are found in hurricanes. Simple-shear flow and the bounded Rankine vortex do not admit discrete modal solutions since there is no mean-state vorticity-gradient to support them. The unbounded Rankine vortex is examined to investigate how the presence of discrete modes (Rossby edge-waves) associated with the radial vorticity-gradient of the Rankine swirl modifies the continuous spectrum solutions presented here.