The Kutta Condition in Unsteady Flow

In several papers published in the first decade of this century, Kutta and Joukowsky independently proposed that the lift on an airfoil at incidence in a steady un separated flow is given by potential-flow theory with the unique value of the circulation that removes the inverse-sQuare-root velocity singularity at the trailing edge. This proposal-tantamount to saying (cf. Batchelor 1967) that in the unsteady start-up phase the action of viscosity is such that, in the ultimate steady motion, viscosity can be explicitly ignored but implicitly incorporated in a single edge condition-is known as the Kutta-Joukowsky hypothesis. Subsequently the name "Kutta condition" (no doubt largely for brevity) has come to be used to connote the removal of a velocity singularity at some distinguished point on a body in unsteady flow. 1 The condition has recently been applied to unsteadiness in a variety of mean configurations. These include trailing-edge flows with the same and with different flows on the two sides of the body upstream of the edge, attached leading-edge flows, and grossly separated flows past bluff bodies. Imposition of a Kutta condition on unsteady perturbations to one of these mean flows has a variety of physical ramifications. It represents the mechanism by which both the lift is changed and the amplitude and directivity of a sound field are modified. It is the analytical step that in many cases describes the conversion-almost total-of acoustic energy in an incident sound wave to energy of vortical motion on a shear layer ; on