The wake in fluid flow past a solid

Abstract

1. A striking feature of modern hydrodynamics is the number of instances where cyclic irrotational motion, with local filaments of vorticity, is used as a valid approximation to the motion of a real fluid. By a real fluid I necessarily mean a viscous fluid. It has been well established, especially in the Kutta-Joukowsky theory of the aerofoil in two dimensions, its generalization to three dimensions by Lanchester and Prandtl, and in Karman’s theory of double rows of travelling vortices, that the results are in good quantitative agreement with experiment, accounting for the forces on an immersed solid in all directions with respect to the general flow of the current. The existence of cyclic motion is in disagreement with classical hydrodynamics, which predicts that there shall be no circulation about any circuit drawn in a fluid initially at rest or in uniform motion, and that there is no resultant thrust on a solid immersed in a steady uniform current. Considerable attention has been given to the reason why classical hydrodynamics fails to represent the experimental facts; but it appears to me that these efforts arise from an incorrect point of view. The classical fluid differs from the real fluid in two fundamental respects. It can slip freely over a solid boundary without resistance; the actual fluid has no velocity relative to any solid surface in contact with it. In the classical fluid, the stress across any small surface element within the fluid is exactly perpendicular to that element; in the real fluid it is, in general, inclined to it. In one respect, the classical fluid is more constrained than the real fluid; in the other it is less so. In these circumstances, the remarkable thing is not that classical hydrodynamics is often wrong, but that it is ever nearly right. Classical hydrodynamics ceased to be a representation of the physical facts when Poiseuille showed that liquid flowing through a capillary tube was at rest when in contact with the sides of the tube.