Unsteady flow over a decelerating rotating sphere

Abstract

Unsteady flow analysis induced by a decelerating rotating sphere is the main concern of this paper. A revolving sphere in a still fluid is supposed to slow down at an angular velocity rate that is inversely proportional to time. The governing partial differential equations of motion are scaled in accordance with the literature, reducing to the well-documented von Kármán equations in the special circumstance near the pole. Both numerical and perturbation approaches are pursued to identify the velocity fields, shear stresses, and suction velocity far above the sphere. It is detected that an induced flow surrounding the sphere acts accordingly to adapt to the motion of the sphere up to some critical unsteadiness parameters at certain latitudes. Afterward, the decay rate of rotation ceases such that the flow at the remaining azimuths starts revolving freely. At a critical unsteadiness parameter corresponding to s = −0.681, the decelerating sphere rotates freely and requires no more torque. At a value of s exactly matching the rotating disk flow at the pole identified in the literature, the entire flow field around the sphere starts revolving faster than the disk itself. Increasing values of -s almost diminish the radial outflow. This results in jet flows in both the latitudinal and meridional directions, concentrated near the wall region. The presented mean flow results will be useful for analyzing the instability features of the flow, whether of a convective or absolute nature.