Tidal dissipation in rotating fluid bodies: the presence of a magnetic field

TL;DR

This study explores how magnetic fields influence tidal dissipation in rotating fluid bodies, revealing that magnetic effects can dominate energy loss mechanisms and alter frequency-dependent dissipation characteristics.

Contribution

It introduces a simplified model with magnetic fields to analyze tidal responses, showing that magnetic damping can dominate and that frequency-averaged dissipation remains unaffected by magnetic field details.

Findings

Ohmic damping can dominate energy dissipation even with weak magnetic fields.

Magnetic fields smooth and broaden the frequency spectrum of dissipation.

Frequency-averaged dissipation is independent of magnetic field strength and structure.

Abstract

We investigate effects of the presence of a magnetic field on tidal dissipation in rotating fluid bodies. We consider a simplified model consisting of a rigid core and a fluid envelope, permeated by a background magnetic field (either a dipolar field or a uniform axial field). The wavelike tidal responses in the fluid layer are in the form of magnetic-Coriolis waves, which are restored by both the Coriolis force and the Lorentz force. Energy dissipation occurs through viscous damping and Ohmic damping of these waves. Our numerical results show that the tidal dissipation can be dominated by Ohmic damping even with a weak magnetic field. The presence of a magnetic field smooths out the complicated frequency-dependence of the dissipation rate, and broadens the frequency spectrum of the dissipation rate, depending on the strength of the background magnetic field. However, the frequency-averaged dissipation is independent of the strength and structure of the magnetic field, and of the dissipative parameters, in the approximation that the wave-like response is driven only by the Coriolis force acting on the non-wavelike tidal flow. Indeed, the frequency-averaged dissipation quantity is in good agreement with previous analytical results in the absence of magnetic fields. Our results suggest that the frequency-averaged tidal dissipation of the wavelike perturbations is insensitive to detailed damping mechanisms and dissipative properties.