Journal Article

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

Harry J. Braviner and Gordon I. Ogilvie

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 441, issue 3, pages 2321-2345
ISSN: 0035-8711
Published online May 2014 | e-ISSN: 1365-2966 | DOI:
Tidal interactions of a Maclaurin spheroid – I. Properties of free oscillation modes

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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 ≤ 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.

Keywords: hydrodynamics; waves; planet–star interactions; binaries: general

Journal Article.  19531 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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