Free waves on barotropic vortices. Part I: Eigenmode structure

Abstract

To understand the nature of coupling between a hurricane vortex and asymmetries in its near-core region, it is first necessary to have an understanding of the spectrum of free waves on barotropic vortices. As foundation for upcoming work examining the nonaxisymmetric initial-value problem in inviscid and swirling boundary layer vortex flows, the complete spectrum of free waves on barotropic vortices is examined here. For a variety of circular vortices in gradient balance the linearized momentum and continuity equations are solved as a matrix eigenvalue problem for perturbation height and wind fields. Vortex eigensolutions are found to fall into two continuum classes. Eigenmodes with frequencies greater than the advective frequency for azimuthal wavenumber n are modified gravity-inertia waves possessing nonzero potential vorticity in the near-core region. Eigenmodes whose frequencies scale with the advective frequency comprise both gravity-inertia waves and Rossby-shear waves. Linearly superposing the Rossby-shear waves approximates the sheared disturbance solutions. For wavenumbers greater than a minimum number, Rossby-shear waves exhibit gravity wave characteristics in the near-vortex region. Although such eigenstructure changes are not anticipated by traditional scaling analyses using solely external flow parameters, a criterion extending Rossby's characterization of "bal-anced" and "unbalanced" flow to that of azimuthal waves on a circular vortex is developed that correctly predicts the observed behavior from incipient vortices to hurricane-like vortices. The criterion is consistent with asymmetric balance theory. Possible applications of these results to the wave-mean-flow dynamics of geophysical vortex flows are briefly discussed.