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Numerical study of viscous modes in a rotating spheroid

Abstract : The motion of an incompressible, viscous rotating fluid contained in an oblate spheroidal container is studied by a direct numerical simulation in an appropriate spheroidal coordinate system and in the linear approximation. The behaviour of a few eigenmodes is investigated as a function of the eccentricity e of the container, for a Ekman number E = 10-5. Viscous effects are evidenced through internal shear layers, the spatial structure of which strongly depends on the eccentricity. In particular, for the spin-over mode, a resonance occurs around a critical value ec ! 0.50, where the decay rate strongly deviates from the predicted theoretical variation. This resonance is discussed in relation with the accidental coincidence between the spin-over frequency and two other frequencies corresponding to the (8,1,5) and (14,1,9) inertial eigenmodes.
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Denys Schmitt. Numerical study of viscous modes in a rotating spheroid. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2006, 567, pp.399-414. ⟨10.1017/S0022112006002497⟩. ⟨insu-00196706⟩

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