Effect of secondary flow on the decaying torsional oscillations of a sphere and a plane

The correction to the torque on a torsionally oscillating sphere in a viscous fluid due to the induced secondary flow is calculated when the thickness of the shear layer is small compared with the radius of the sphere. The calculations correct an error in the formulas given by Carrier and DiPrima. Using the method of multiple scales, the effect of finite amplitude on the logarithmic decrement and added moment of inertia of the sphere are obtained for the decaying oscillations of the sphere. The results are in good agreement with the experimental measurements of Folse, Strahan, and Nail. Similar formulae are given for the decaying oscillations of a plane.