Numerical study of viscous modes in a rotating spheroid

Denys Schmitt (1)

1 LGIT - Laboratoire de Géophysique Interne et Tectonophysique

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.

Keywords: Rotating flows; Navier-Stokes equations; Waves in rotating fluids

Domains: Geophysics [physics.geo-ph]; Fluid mechanics [physics.class-ph]

Denys Schmitt. Numerical study of viscous modes in a rotating spheroid. Journal of Fluid Mechanics, 2006, 567, pp.399-414. ⟨10.1017/S0022112006002497⟩. ⟨insu-00196706⟩