FREE WAVES ON BAROTROPIC VORTICES .1. EIGENMODE STRUCTURE

To understand the nature of coupling between a hurricane vortex and as ymmetries in its near-core region, it is first necessary to have an un derstanding of the spectrum of free waves on barotropic vortices. As f oundation for upcoming work examining the nonaxisymmetric initial-valu e problem in inviscid and swirling boundary layer vortex flows, the co mplete 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 p roblem for perturbation height and wind fields. Vortex eigensolutions ale found to fall into two continuum classes. Eigenmodes with frequenc ies greater than the advective frequency for azimuthal wavenumber n ar e modified gravity-inertia waves possessing nonzero potential vorticit y in the near-core region. Eigenmodes whose frequencies scale with the advective frequency comprise both gravity-inertia waves and Rossby-sh ear waves. Linearly superposing the Rossby-shear waves approximates th e sheared disturbance solutions. For wavenumbers greater than a minimu m number, Rossby-shear waves exhibit gravity wave characteristics in t he near-vortex region. Although such eigenstructure changes are not an ticipated by traditional scaling analyses using solely external how pa rameters, a criterion extending Rossby's characterization of ''balance d'' and ''unbalanced'' flow to that of azimuthal waves on a circular v ortex is developed that correctly predicts the observed behavior from incipient vortices to hurricane-like vortices. The criterion is consis tent with asymmetric balance theory. Possible applications of these re sults to the wave-mean-flow dynamics of geophysical vortex flows are b riefly discussed.