University of Western Ontario
London, Ontario, Canada
It is well known that the determination of the circulation in two-dimensional flow past a cylinder is indeterminate in the case of an inviscid fluid governed by potential theory and must be chosen arbitrarily except in specific cases, such as the case of an aerofoil with a sharp trailing edge. In that case the circulation may be chosen to eliminate a singularity in the flow field which would lead to a violation of a physically realistic flow. Moreover, it is known that physically realistic two- dimensional flows do exist by means of careful experiments which visualize the flows and assist in verifying many of the detailed flow properties and basic theorems of fluid mechanics which govern the motion. In this presentation we shall first examine the general indeterminacy of the circulation in inviscid two- dimensional flows and then turn to the problem of the flow of a viscous fluid to see what information can be derived in that case. Some problems of both unsteady and steady viscous, incompressible, flows will be considered as examples and a discussion will be given as to what conditions must be satisfied in order to determine the circulation in any general case of a two-dimensional incompressible flow assumed to be governed by the Navier-Stokes equations.