Turbulent dissipation in the boundary layer of precession-driven flow in a sphere

Abstract

The energy dissipation in a uniform vorticity flow, such as the flow in a precessing spheroid or the one associated with the earth’s free core nutation, is mainly confined to the boundary layers. However, the thinness of the boundary layer renders it difficult to study the energy dissipation in the turbulent regime, either in laboratory experiments or through direct numerical simulations. Here, we use a local Cartesian model to study the energy dissipation in the boundary layer of a precessing sphere when the flow becomes turbulent, contrasting it with the laminar case. We compute the evolution of the boundary layer over time at individual co-latitudes based on direct numerical simulations using the computational fluid dynamics solver Nek5000. We then estimate the total global dissipation by summing up individual contributions. A comparison with known analytical results in the laminar case validates this approach. We briefly discuss the applications to the lunar and the earth’s core cases.

Special topic on precession, nutation, and libration driven flows

“…The field of rotating non-linear dynamics, weak or strong, is very active with a broad range of applications. It has been established that non-linear interactions in rotating fluid cavities may lead to boundary layer 5 or bulk instabilities, 6,7 which govern the turbulent dissipation, and when the fluid is electrically conductive to magnetic field generation. Subbotin et al 7 have studied in detail the non-linear interactions in an annulus with a precessing lid at the top of the cavity.…”