Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 441, Issue 3, Pages 2321-2345Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stu704
Keywords
hydrodynamics; waves; planet-star interactions; binaries: general
Categories
Funding
- STFC
- Trinity College
- STFC [ST/J001570/1, ST/L000636/1] Funding Source: UKRI
- Science and Technology Facilities Council [ST/L000636/1, ST/J001570/1] Funding Source: researchfish
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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 a parts per thousand currency sign 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. We see that the equatorial bulge of the spheroid has a significant effect on the decay rates (changing some of these by a factor of 2 between an eccentricity of e = 0 and 0.5), and a more modest effect on the mode frequencies. This suggests that models of tidal interaction between rapidly rotating stars and giant planets that model the Coriolis force while neglecting the centrifugal distortion of the body may be in error by an order unity factor. In a subsequent paper, we shall examine the case of a forced flow in this spheroid, and complete the model by considering how the tides raised by the orbiting companion change the orbital elements.
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