Viscous Damping Forces on Oscillating Cylinders

Theoretical descriptions have been derived for the fluid force on a sinusoidally vibrating cylinder. The descriptions were obtained by applying perturbation expansion techniques to the Navier-Stokes equations based on small amplitude-to-radius ratio = e/a and large vibratory Reynolds number R = a2 ¿/¿, where ¿ is frequency of vibration and ¿ is kinematic viscosity. By developing solutions for higher-order terms in the perturbation expansion involving , information was obtained on the behaviour of the hydrodynamic force as increases. Results derived, supplemented with experimental evidence, indicate that the hydrodynamic damping force changes rather abruptly from viscous damping as described by Stokes, to much larger quadratic fluid drag at = 0(1).