Asymptotic solutions for the motion of a viscous incompressible fluid filling the cavity of a rotating body

Asymptotic solutions are obtained for the motion of a nonuniformly heated fluid of high viscosity and high thermal diffusivity wholly or partially filling the cavity of a rotating body. It is shown that, when the fluid wholly fills the cavity, nondamped perturbations of velocity and temperature arise in the second approximation which are the result only of transport and Coriolis forces. When the cavity is partially filled, there arise in the first approximation slowly damped perturbations, induced by the presence of a free surface and the initial field of fluid velocity and temperature.