Steady Rotational Flow of an Incompressible, Viscous Fluid Enclosed between Two Coaxial Cylinders

Abstract

This paper gives a theoretical study of the two-dimensional flow of an incompressible, viscous fluid enclosed between two coaxial cylinders, one of which is oscillating. The Reynolds number is assumed to be small, and the Navier-Stokes differential equations are solved by means of the method of successive proximations. Both for the first and second order solution the proper boundary conditions are applied. We have shown that there exist two stationary circulation systems in every quadrant, and that the direction of circulation is opposite in these two systems. The circulation velocities are calculated in detail, and the results are compared with experimental results referred to in an earlier paper. Some new experimental results, which are not published yet, are briefly mentioned. The agreement between theoretical and experimental results is excellent. In a discussion at the end of the paper we give the explanation of the remarkable fact that in some experiments the direction of circulation seems to reverse when the oscillation amplitude increases and exceeds a certain critical value.