11:00 am–12:00 pm
Alexander Bogatskiy’s PhD Thesis Defense
Thursday June 3, 2021 at 11:00 AM CDT
VORTEX FLOWS ON SURFACES AND THEIR ANOMALOUS HYDRODYNAMICS
Hydrodynamic flows with large numbers of vortices have been a staple of theoretical hydrodynamics starting with superfluids, Onsager, and Feynman. Treating such vortices as constituents of a new fluid of their own leads to an interesting anomalous hydrodynamics that exhibits curious phenomena such as odd viscosity. Starting with the incompressible Euler equation, I rigorously derive the entire coarse-grained hydrodynamics of the "vortex matter" consisting of many identical discrete point vortices on an arbitrary closed 2D surface. The resulting flow of vortices differs from the original flow of the underlying fluid by a term that can be related to odd viscosity and also leads to a particular interaction between the vortex density and the scalar curvature. When considering bounded droplets of vortex matter, one also finds unexpected static and dynamic features at the edge of the droplet — the so called "overshoot". I will briefly describe a certain chiral solitonic mode propagating within the overshoot.
Committee members
Paul Wiegmann (Chair)
William Irvine
Vincenzo Vitelli
Mark Oreglia
Alex will be starting a postdoc at the Flatiron Institute developing physics-informed machine learning methods for scientific applications such as particle physics and condensed matter.