Tidal interactions of a Maclaurin spheroid. I: Properties of free oscillation modes

Understand

We review the work of Bryan (1889) on the normal modes of a Maclaurin spheroid, carrying out numerical calculations of the frequencies and spatial forms of these modes that have not been previously published.

• We study all modes of degree $l \le 4$, which includes both inertial modes and surface gravity modes, with the aim of better understanding the effect of rapid rotation on tidal interactions.
• The inclusion of these higher degree modes greatly increases the number of frequencies at which tidal resonances may occur.
• We derive an expression for the decay rates of these modes to first order in viscosity and explicitly plot these for modes.