Bistable flows forced by precession in planetary cores

Abstract:

The presence of the Moon leads the Earth to precess, which forces a flow in its outer core via the spheroidal Core-Mantle Boundary (CMB). Reciprocally, this is also true for the liquid core core of the Moon, but the CMB is rather a triaxial ellipsoid in this case.

In this work, we investigate if the precession can force two different stable flows for the same control parameters, allowing then the core to switch from one state to the other in presence of noise (convection, turbulence, etc.). To do so, we systematically study the parameter ranges where the well-known equations obtained by Busse (1968 J. Fluid Mech. 33 739–51) lead to multiple solutions. Then, using the models recently proposed by Noir and Cébron (2013 J. Fluid Mech. 737 412–39), which are more generic in the inviscid limit than the equations of Busse, we analytically describe these multiple solutions, their conditions of existence, and their stability. We also report for the first time the theoretical possibility that time-dependent multiple flows can coexist in precessing triaxial ellipsoids (such as the liquid core of the Moon).

Finally, using the formula we have derived from pre-existent models of the literature, we conclude that the Earth and the Moon do not undergo such a bistable flow forced by precession. However, according to the models of the literature, such a bistable precession forced state exists for geophysically relevant ranges of parameters, and is thus always possible a priori in precessing liquid cores of terrestrial bodies.