Steady flow in a rapidly rotating sphere with weak precession

Abstract

The flow field of an incompressible viscous fluid in a precessing sphere is investigated by the asymptotic analysis for large Reynolds numbers and small Poincaré numbers. The long-standing unsolved equation (Roberts & Stewartson Astrophys. J., vol. 137, 1963, p. 777) for the velocity in the critical region of the boundary layer is solved for the first time in the literature, which enables us to describe explicitly the structure of the conical shear layers spawned from the critical regions into the interior inviscid region. Most of the flux between the boundary layer and the interior is taking place through these conical shear layers. The velocity field in the whole sphere, expanded in a power series of the Poincaré number, is quantitatively determined up to the first order, leaving the solid-body-rotation component to the next-order analysis.