Nonlinear Core-Mantle Coupling

Abstract

We explore the nonlinear dynamics of a forced core-mantle system. We show that the free axisymmetric motion of a uniform-vorticity fluid core coupled to a rigid mantle (the Poincaré-Hough model) is integrable. We derive an approximate Hamiltonian for the core tilt mode that includes the leading nonlinear contribution. We then include gravitational perturbations in the analysis. We identify the principal nonlinear prograde and retrograde resonances and the characteristic excitation associated with each. We compare the nonlinear excitation with the excitation expected in the corresponding linear model. The nonlinear model indicates that for each principal commensurability there are multiple overlapping resonances, and so varying degrees of chaotic behavior are predicted. Chaotic behavior at the principal core-mantle commensurabilities is confirmed with surfaces of section. We then present the results of numerical evolutions done with a generalization of our (1994) Lie-Poisson integrator to allow for a Poincaré-Hough core, core-mantle friction, and tidal dissipation. We use our analytical and numerical models to explore the evolution of Earth through the prograde core-mantle resonances and to explore the evolution of Venus through the retrograde resonances. Heating of the core-mantle boundary during resonance passage is much greater for Venus than for Earth. We raise the question whether heating during core-mantle resonance passage could be responsible for the global resurfacing of Venus.