Vortical Structures Using Fundamental Solutions of the Stokes Equations*

The Burgers vortex, while satisfying the Navies-Stokes equations, allows for vorticity gradients, finite net diffusion of vorticity, and small radii of curvature of streamlines. These features are ideal to use as a model unit of turbulent flow around swimming microorganisms. Several experimental setups have also been proposed to create Burger’s vortex-like structures in the lab using submerged rotating disks and mechanisms to create vortex stretching. In this work, we model the lower limit of these rotating disk setups and use regularized fundamental solutions of Stokes’ equations to produce vortical structures. Several solutions are proposed that mimic the experimental setup using different combinations of fundamental solutions of varying orders. This approach allows us to reproduce spatial vorticity and azimuthal velocity distributions that are highly comparable to the analytical Burger’s vortex results. We then test the behavior of actuated and passive flexible filaments in this vortex at different strengths and examine the resulting shape evolution and trajectories.