Spin Down of Boussinesq Fluid in a Circular Cylinder

Abstract

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing circular cylinder under the existence of stable distribution of the temperature is investigated within the frame work of Boussinesq approximation for the time duration of the order of the incompressible spin down time. The coexistence of a horizontal intermediate adjusting layer together with the Ekman layer is clarified as a characteristic feature of unsteady motion. The asymptotic amount of the total angular momentum transferred to the main bulk of the fluid is investigated in detail, and it is shown that the spin down phenomenon similar to that in the incompressible fluid does occur even for cases which are classified as compressibility dominant according to the behavior of steady motion.