Surface tide on a rapidly rotating body

TL;DR

This paper investigates how rapid rotation affects surface tides on celestial bodies by solving tidal equations numerically, revealing the emergence of resonances at high rotation speeds and their dependence on friction and fluid layer thickness.

Contribution

It provides a numerical analysis of surface tides on rapidly rotating bodies, extending previous asymptotic results to cases with significant rotational effects.

Findings

Tidal resonances become prominent at high rotation rates ($.1$)

Friction reduces but does not eliminate tidal resonances at fast rotation

Fluid layer thickness influences tidal resonances, especially at slower rotation

Abstract

By solving Laplace's tidal equations with friction terms we study the surface tide on a rapidly rotating body. When $\epsilon=\Omega^2 R/g$, the square of the ratio of dynamical timescale to rotational timescale, is very small for the Earth the asymptotic result was derived. When it is not so small, e.g. a rapidly rotating star or planet, we perform numerical calculations. It is found that when rotation is sufficiently fast ($\epsilon$ reaches $0.1$) a great amount of tidal resonances appear. To generate the same level of tide, a faster rotation corresponds to a lower tidal frequency. Friction suppresses tidal resonances but cannot completely suppress them at fast rotation. The thickness of fluid layer can change tidal resonances but this change becomes weaker at faster rotation. This result is of help to understanding the tides in the atmosphere of a rapidly rotating star or planet or in the ocean of a neutron star.