On fluid motion in librating ellipsoids with moderate equatorial eccentricity

The motion of a homogeneous fluid of viscosity nu confined in a librating ellipsoidal cavity with semi-axes a and moderate equatorial eccentricity E is investigated. The ellipsoid rotates with an angular velocity Omega(0)(1 + d delta sin (omega) over capt), where Omega(0) is the mean rate of rotation, (omega) over cap is the libration frequency and Omega(0)delta represents the amplitude of longitudinal libration. When delta << E-2 and E-1/2 << E-2 << 1, where E is the Ekman number defined as E = nu/(a(2)Omega(0)), an explicit analytical solution describing fluid motion in librating ellipsoids is derived for any size of the libration frequency (omega) over cap. 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.