Absorption and reflection of inertial waves by a geostrophic vortex

Physics of Fluids. 2025. Vol. 37. No. 12. Article 126605.

Nikolay A. Ivchenko, Vergeles S. S.

Interaction of inertial waves with geostrophic flow in a rapidly rotating fluid system is studied. In accordance with the experimental conditions [Tumachev et al., “Two dynamical regimes of coherent columnar vortices in a rotating fluid,” JETP Lett. 118, 426 (2023) and Tumachev et al., “Observation of a large stable anticyclone in rotating turbulence,” Phys. Fluids 36, 126620 (2024)], this study addresses inertial waves that are excited near the side boundary of the flow and enter the region where geostrophic vortex flow is present. The wave equation is derived and analyzed, which describes the propagation of convergent and divergent cylindrical waves on the background of axisymmetric mean vortex flow. It is shown that a monochromatic wave does not exert any torque on the vortex flow in the inviscid limit until it is absorbed inside its critical layer. Among convergent waves, those only are absorbed, which carry 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 wave absorption is possible only if the vortex flow is characterized by fast enough angular velocity there. The behavior of wave near the critical layer is described by the well-known model, where the mean flow is the rectilinear shear flow. It is shown that the conventional wave train approximation for the short-wave limit is not applicable in the vicinity of the layer and revised by deriving the proper equation and reformulating conservation law of the wave action. For the vicinity of the critical layer, a model accounting for viscous dissipation is derived; viscous effects are studied for the absorption of both monochromatic wave and wave train.

Keywords: турбулентность, вихревые течения, эффект Доплера, WKB-approximation, Doppler effect, vortex flows, rotating flows, циклоны и антициклоны, энергетический обмен, inertial waves, инерционные волны, Viscous fluids, wave energy transfer