A variational approach to modeling a cylinder in ground effect

For high Reynolds number flow over a cylinder near a moving surface, a potential flow model can be used to represent flow over the leading edge. However, the potential flow solution requires knowledge of the circulation around the cylinder. This circulation value can be found with an auxiliary condition using an energy method. Multiple choices for this variational condition exist. Gol'dshtik & Khanin (1978) postulated an ad-hoc variational approach that looks only at the velocity on the cylinder boundary. Guided by the novel work of Gonzalez & Taha (2022), we consider an extension of Gauss' principle that takes into account the entire velocity field. We will compare the predictions of these two models with experiments by considering the pressure distribution and forces on the cylinder as a function of proximity to the wall. We also discuss improvements to the model predictions through ad-hoc inclusion of flow separation.