Unsteady Boundary Layers : 2 nd Report, Flow around a Body with a Fluctuating Circulation

Abstract

Unsteady boundary layers, caused by a fluctuating circulation, are investigated theoretically. Incompressible, two-dimensional, laminar flow is assumed. Further assumption is made that the magnitude of velocity fluctuation is small compared with the mean velocity and that the frequency of fluctuation is low. Blasius'series method of solution of the boundary layer equations is extended to the unsteady flow. Detailed calculation is shown of the flow around a body symmetrical, with velocity fluctuation outside the boundary layer antisymmetrical, with respect to the undisturbed stream. As in the steady flow problem, the solution of the unsteady boundary layer equation can be expressed as a linear combination of a set of universal velocity distribution functions. Four of the functions are actually computed, by use of which boundary layer separation from a circular cylinder with circulation fluctuation is discussed. The separation point movement is found to consist of a quasisteady and an unsteady components, the latter increasing with frequency.