Vortex Shedding and Low Order Models

Vortex shedding is of fundamental interest in fluid dynamics, with many applications in physics, engineering, and biology, with relevance for example in biolocomotion. Numerical studies of separated flows using the full governing equations are numerically expensive, and in practice, low order approximations such as point vortex or vortex sheet models are often used instead. These models are based on simple algorithms used to satisfy the Kutta condition at sharp edges. The goal of the work I will present is to use highly resolved direct numerical simulations of flow normal to a finite flat plate to better understand detailed aspects of the flow and to obtain benchmark results to evaluate lower order models. Some of the details of the flow evolution revealed by the simulations include the presence and duration of an initial Rayleigh stage. This stage is characterized by a boundary layer of vorticity of almost constant thickness that surrounds the tip of the plate. After this initial period, vorticity concentrates near the tip forming a starting vortex that grows and eventually separates from the boundary vorticity. Using the simulations, we obtain values for the shed circulation, vortex trajectory and vortex sizes as a function of time and Reynolds number. We then compare the viscous results for accelerated flow past a flat plate with results obtained using the vortex sheet model, and determine the extent
to which the model reproduces the flow.