Modeling unsteady aerodynamics: an unsteady Kutta condition or the principle of minimum curvature?

The classic Kutta condition removes the velocity singularity at the sharp trailing edge and provides a unique solution for the lift on a streamlined body in a steady potential flow. The extension of the Kutta condition to unsteady flows has received much criticism since its conception, and fluid mechanicians often select a particular variation of the Kutta condition to suit a specific unsteady problem. Although there are unsteady problems for which a simple extension of the Kutta condition has proven valuable, researchers do not have a common consensus for what constitutes a generalized unsteady Kutta condition. Recently, an alternative approach has been proposed based on the variational mechanics principle of minimum curvature or pressure gradient [Gonzalez & Taha 2022 JFM 941 A58]. Compelling evidence in support of this theory is provided for streamlined bodies with rounded trailing edges, but no discussion has yet been presented in the literature that extends this approach to unsteady flows. We explore the application of various extensions of the Kutta condition and this new variational approach to determining the time-dependent lift force on an oscillating plate.