Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Abstract

The purpose of this paper is to discuss qualitatively certain kinds of asymptotic motion in a two-dimensional, ideal fluid by help of methods of statistical mechanics. It is stressed that the final development of such a fluid cannot be adequately described by use of the ordinary equations of motion, but that a “coarse grain” representation should be used. In this representation, the development is characterized by the forming of a single, large vortex accompanied by a certain non-viscous dissipation. The final equilibrium is probably reached almost explosively after a finite time. Some experiments which are carried out seem to support this result. In the earlier stages of development we may expect to have some kind of a quasi-equilibrium motion. It is attempted to find conditions under which such a motion can exist, by studies of a point-vortex model. DOI: 10.1111/j.2153-3490.1955.tb01147.x