Rotating Modons over Isolated Topographic Features

Abstract

In this paper steadily rotating modons that are trapped over topographic features with finite horizontal length scales are described. The quasigeostrophic equation over topography is transformed to a frame rotating with angular frequency ?, and steady solutions are sought that decay monotonically outside of a circle of radius, r=ra. These conditions are imposed upon an isolated seamount or depression of the form ?=h0[1?(r/rb)m] (and ?=0 for r≥rb) with primary focus on the m=2 case. Two different scenarios result from this choice of topography and correspond to ra/rb=α½≥1 or α½≤1. There are three solution regions compared with the usual two for rectilinear modons. Both scenarios result in a countable infinity of both radial and azimuthal modes. In addition, it is found that an axisymmetric flow with a particular form but arbitrary amplitude can be added to the basic modon multipole solutions. The angular frequency is then found as a function of α and this axisymmetric flow amplitude. Topographically trapped rotating modons can spin clockwise or anticlockwise.