Two-dimensional Brinkman flows and their relation to analogous Stokes flows

Abstract 2D Stokes flows often exhibit the Stokes paradox: logarithmic growth of the fluid velocity in the far field. Analogous Brinkman flows are governed by the same equations apart from an additional term involving a parameter $\alpha$. Although these equations reduce to those for Stokes flow when $\alpha =0$, we show that the Brinkman solutions do not approach the corresponding Stokes solutions as $\alpha \to 0$; instead, logarithmic divergence with $\alpha$ is found. We also show that Brinkman flows do not exhibit a Stokes-like paradox. These results are given in detail for two specific problems, namely flow past a rigid circular cylinder and flow past a thin rigid strip.