Mean flow induced by longitudinal libration of a fluid-filled rotating container bounded by two conical surfaces

The problem of determining a mean flow induced by longitudinal libration of a rapidly rotating fluid-filled container bounded by the surfaces of two oppositely oriented right circular cones is considered. It is shown that the problem is reduced, through introducing a cosine of the angle between the normal to the conical surfaces and the axis of rotation, to the problem of determining a mean flow induced by libration of a fluid-filled rotating cylindrical container of infinite radius. A theoretical scenario is proposed of how the solved problem can be applied to the approximate determination of the differential mean rotation in a significant part of a rotating spherical and/or oblate spheroidal cavity under the action of longitudinal libration forcing.