Tidal dissipation in rotating fluid bodies: a simplified model

TL;DR

This paper models tidal dissipation in rotating fluid bodies using a simplified setup to analyze inertial wave propagation and dissipation, revealing complex frequency-dependent behaviors relevant to planetary and stellar dynamics.

Contribution

It introduces a simplified model for inertial wave dissipation in rotating fluids, highlighting the dependence on core size and frequency, and discusses wave features affecting dissipation efficiency.

Findings

Dissipation rate varies complexly with tidal frequency.

Efficient dissipation occurs even with very low viscosity in certain frequency ranges.

Core size influences the dissipation magnitude.

Abstract

We study the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body. The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous incompressible fluid. Centrifugal effects are neglected, but the Coriolis force is considered in full, and dissipation occurs through viscous or frictional forces. The dissipation rate exhibits a complicated dependence on the tidal frequency and generally increases with the size of the core. In certain intervals of frequency, efficient dissipation is found to occur even for very small values of the coefficient of viscosity or friction. We discuss the results with reference to wave attractors, critical latitudes and other features of the propagation of inertial waves within the fluid, and comment on their relevance for tidal dissipation in planets and stars.