Absorption and reflection of inertial waves by a geostrophic vortex

Abstract

We study interaction of inertial waves with geostrophic flow in a rapidly rotating fluid system. In accordance with experimental conditions in [1, 2], we consider inertial waves, which were excited by a source being near side boundary of the flow and enter the region where geostrophic vortex flow is present. The wave equation is derived and analyzed in the paper that describes the propagation of convergent and divergent cylindrical waves on the background of mean vortex flow, which is considered as an axisymmetric differential rotation. We show that a monochromatic wave does not exert any torque on the vortex flow in the inviscid limit until it is absorbed inside the critical layer. Among convergent waves those only are absorbed which carries angular momentum of the same sign as one's of the rotation in the vortex. Convergent waves with the opposite sign of angular momentum are just reflected from the vortex. The absorption of a wave is possible only if the vortex flow is characterized by fast enough angular velocity there. The behavior of the wave near the critical layer can be described by the well-known model where the mean flow is rectilinear shear flow. We show that the conventional wave train approximation for the short-wave limit is not applicable in the vicinity of the layer and revise it, deriving the proper equation and reformulating the conservation law of wave action. For the vicinity of critical layer, a model which accounts for the viscous dissipation is derived; viscous effects are studied for absorption both of monochromatic wave and wave train.