Inertial Modes in Near-Spherical Geometries

Abstract

We propose a numerical method to compute the inertial modes of a container with near-spherical geometry based on the fully spectral discretisation of the angular and radial directions using spherical harmonics and Gegenbauer polynomial expansion respectively. This allows to solve simultaneously the Poincare equation and the no penetration condition as an algebraic polynomial eigenvalue problem. The inertial modes of an exact oblate spheroid are recovered to machine precision using an appropriate set of spheroidal coordinates. We show how other boundaries that deviate slightly from a sphere can be accommodated for with the technique of equivalent spherical boundary and we demonstrate the convergence properties of this approach for the triaxial ellipsoid.

References in corpus (4)

• Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
• A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid
• Completeness of Inertial Modes of an Incompressible Non-Viscous Fluid in a Corotating Ellipsoid
• The coupling between inertial and rotational eigenmodes in planets with liquid cores

Cited by in corpus (5)

• Internal energy dissipation in Enceladus's ocean from tides and libration and the role of inertial waves
• Identification of inertial modes in the solar convection zone
• The coupling between inertial and rotational eigenmodes in planets with liquid cores
• Inertial modes of a freely rotating ellipsoidal planet and their relation to nutations
• Acoustic and inertial modes in planetary-like rotating ellipsoids