On the Frictional Damping of the Rolling of a Circular Cylinder

The frictional damping of the rolling motion of a circular cylinder is nonlinear. Although negligible at full scale, it may be important in model scale. The damping force is calculated using Fourier analysis of the frictional force on the surface of a cylinder with a vertical axis executing simple harmonic oscillations about its axis. Calculations of the velocity profile in the fluid near the oscillating cylinder, needed for the calculations of the frictional force, are carried out in the laminar and turbulent case using the boundary-layer approximation. For Reynolds shear stress modeling, the mixing length concept of Prandtl and an analogy to van Driest's model are used. The resulting nonlinear partial differential equation of the parabolic type is solved numerically using the Du Fort-Frankel explicit finite-difference scheme.