III. On the motion of circular cylinders in a viscous fluid

Abstract

The flow of viscous fluids has been dealt with in numerous mathematical researches. Unlike most other branches of theoretical physics, rational hydrodynamics entails complications due to the non-linearity of the equations of motion, and—in comparison with the effort expended—relatively inconsiderable advance has been made. In the standard “ slow motion ” treatment the product, or inertia, terms of the equations are neglected, by means of which artifice some of the outstanding difficulties are conveniently circumvented. However, even with this simplification, comparatively few solutions to problems have been published. The need for a wider range of results of this particular type became apparent in connection with an ulterior investigation, which will be specified shortly. The present paper is preliminary in this sense, that it deals mainly with such “ slow-motion " problems, and only briefly with the extensions in view. On the other hand, the results, even in the immature stage, need not be without some immediate application, notably to problems relating to fluids of great viscosity. Solutions of this nature admit a further useful interpretation in connection with the deflection of an unloaded flat plate—but the application to elastic theory is outside the range of the paper.