On fluid motion in librating ellipsoids with moderate equatorial eccentricity

The motion of a homogeneous fluid of viscosity ν confined in a librating ellipsoidal cavity with semi-axes a and moderate equatorial eccentricity is investigated. The ellipsoid rotates with an angular velocity Ω 0 (1 + δsin t ), where Ω 0 is the mean rate of rotation, is the libration frequency and Ω 0 δ represents the amplitude of longitudinal libration. When δ ≪ 2 and E 1/2 ≪ 2 ≪ 1, where E is the Ekman number defined as E = ν/( a 2 Ω 0 ), 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.