Ekman boundary layers in a fluid filled precessing cylinder

Abstract

The fluid flow in a precessing cylinder is investigated numerically with focus on the Ekman boundary layers in the strongly forced regime. Not surprisingly, in that regime, we find deviations from the linear theory due to significant modifications of the base flow in terms of an axisymmetric geostrophic mode whose rotation is opposite to that of the container. The transition of the bulk flow from a three-dimensional non-axisymmetric base flow to a geostrophic axisymmetric pattern is reflected in the scaling of both the sidewall boundary layers and the Ekman boundary layers on top and bottom of the cylinder. In our simulations, the Ekman layers surpass the threshold of the first instability (class A) and show an increase in the thickness together with a marked vertical flow advection inside the boundary layer in a limited range of the forcing magnitude. However, due to numerical restrictions in our simulations, which limit the range of achievable Ekman numbers, no developed boundary layer turbulence is found. An estimation by extrapolation shows that, for this purpose, Ekman numbers smaller by a factor of two have to be achieved.