Zoom Meeting: https://unm.zoom.us/j/93108685209 

Password: contact the organizer

Title: Modeling Point Vortices and Vortex Patches under Free-Surface Waves

 

Abstract: The problem of modeling free fluid surfaces is a problem with a rich and lengthy mathematical history.  Traditionally, to make progress, the bulk of the fluid is treated as inviscid and irrotational, thereby allowing for significant mathematical simplifications throughout the majority of the fluid.  However, this is a drastic physical simplification and greatly limits the applicability of many classic free-surface models.  

 

Therefore, in this talk we first explore how to cope with the presence of point vortices in the bulk of the fluid.  Our models leverage classic analytic function techniques and more modern approaches such as the AFM free-surface representation and the concomitant Dirichlet-to-Neumann operator expansions needed to track the free surface dynamics.  Interest in such models stems from point-vortices serving as approximations themselves to more complicated vortical structures.  We examine the impact of various point vortex configurations on both traveling waves and initially quiescent surfaces.  Given the control we have over the simulation, we are able to make careful measurements of the energetic dynamics of the waves as a result of their interaction with the underwater vortices.  

 

Building off of these results, by employing fast-multipole type methods, we are able to extend our point vortex simulations to include more extended vortical structures such as patches.  We then examine for a range of patch strengths how travelling surface waves are attenuated while moving over patches and in turn how vortex patches are deformed by traveling waves.  As expected, strong vortex patches are able to markedly reduce wave amplitude at the expense of the patch appearing to move towards pinching phenomena.  Such results, while preliminary, are some of the most detailed explorations of the interactions between free surfaces and vortical structures, and they point towards many more interesting phenomena.