event
Thursday 13 May 2010: Planetary Precession: Theory and Simulation
Dr Keke Zhang - University of Exeter, UK
Physics, 4th Floor interaction area 14:00-15:00
Many planets like the Earth rotate rapidly and their liquid cores are in the shape of an ablate spheroid. Because of the interaction between planets, moons and their parent stars, those planets are also rotating non-uniformly. In consequence, fluid motion in the planetary liquid cores can be driven by non-uniform rotation such as precession. We consider a viscous, incompressible fluid confined in a spheroidal cavity of arbitrary eccentricity rotating rapidly about its axis of symmetry with angular velocity Omega that itself precesses slowly about an axis fixed in an inertial frame. The precessional problem is mainly characterized by three parameters: the Ekman number E, the Poincare number Po and the eccentricity of the cavity e. When E and |Po| are sufficiently small, we derive a time-dependent asymptotic solution satisfying the non-slip boundary condition in the mantle frame of reference for a spheroid of arbitrary eccentricity. No prior assumption about the spatial-temporal structure of the precessing flow is made in the asymptotic analysis. A solvability condition is derived to determine the spatial structure of the precessing flow, via a selection from a complete spectrum of spheroidal inertial modes in the mantle frame. Direct numerical simulation of the same precessional problem in the same frame of reference, using an EBE (Element-By-Element) finite element method that is suitable for a spheroidal cavity of arbitrary eccentricity, is also carried out. It is shown a satisfactory agreement between the asymptotic solution and the nonlinear numerical simulation is reached for sufficiently small Poincare numbers. The precessing flow on a spheroidal surface within the bulk of the fluid consists of two large vortices centering in the equatorial plane and moving retrogradely. As the Poincare number increases, the centers of the vortices shift from the equator towards finite latitudes, a character consistent with the observations of existing experimental studies.
