Experimental and theoretical study of the steady streaming in a sphere subject to periodic torsional oscillations

We study by theoretical and experimental means the steady streaming generated in a sphere subject to periodic torsional oscillations. The experimental setup consists of a Perspex cylindrical container in which a spherical cavity is carved. The container is filled with glycerol and is then set in motion by a computer controlled motor. PIV measurements of the streaming flow are taken on the equatorial plane normal to the axis of rotation. The problem is also studied theoretically by assuming small amplitude rotations and developing a perturbation solution in terms of this small parameter. At second order the steady streaming flow is reproduced. The streaming flow is axis-symmetric and consists of two toroidal circulation cells, one in each hemisphere. Theoretical results and experimental measurements are in very good quantitative agreement.