Integral Representation of Low-Reynolds-Number Hydrodynamics (Study of Stokes' Paradox)

Abstract

The classical Stokes' paradox for the steady creeping flow past a circular cylinder is theoretically investigated on the basis of the Fredholm integral equations in terms of the vorticity and the stream function. In order to circumvent the difficulty associated with the paradox, this study employs extended Stokes solution that includes the wake behavior behind the cylinder. Then, the present approach successfully determines the indeterminate coefficient caused by Stokes' paradox, and the derived Stokes solution is found to converge to the uniform flow as r → ∞, i. e., Stokes' paradox is resolved.