Oscillating Cylinders and the Stokes' Paradox

Measurements are reported of the inertia coefficient k and damping coefficient k′ for a circular cylinder (radius a) oscillating at angular frequency ω in a fluid of kinematic viscosity ν. Good agreement with the theory of Stokes is obtained throughout the range 0.286<(2ν/ωa2)1/2<4.13 even when the Reynolds number R and the relative amplitude are not small compared with 1. Stokes' theory is expressed in terms of modified Bessel functions, and values of k and k′ are tabulated for 0.001<(a2ω/4ν)1/2<0.5. The relation to Stokes' paradox is considered by examining the damping force in the limit (ωa2/ν)1/2≪1. The damping force for a cylinder, unlike that for a sphere, does not reduce to the low R drag in this limit. However, comparison with Lamb's solution of the Oseen equations suggests an expression that agrees well with drag measurements up to R = 2.5.