On fluid motion in librating ellipsoids with moderate equatorial eccentricity

Abstract

The motion of a homogeneous fluid of viscosity confined in a librating ellipsoidal cavity with semi-axes a and moderate equatorial eccentricity is investigated. The ellipsoid rotates with an angular velocity 0(1 + sint), where 0 is the mean rate of rotation, is the libration frequency and 0 represents the amplitude of longitudinal libration. When 2 and E 1/2 2 1, where E is the Ekman number defined as E = /(a 20), an explicit analytical solution describing fluid motion in librating ellipsoids is derived for any size of the libration frequency. Three-dimensional numerical simulations of the same problem are also performed, revealing the generation of mean zonal flow in librating ellipsoidal cavities and showing a satisfactory agreement between the asymptotic and numerical analyses. Copyright © Cambridge University Press 2011.