*Geometric Quantum Hydrodynamics: Understanding energy dissipation through nonlinear waves on quantized vortex filaments

Scott Strong

sstrong@mines.edu

This project aims to understand the connection between continuum fluid mechanics and the nonlinear wave motion of vortex filaments. Specifically, we study the relationship between the dynamical behavior of helical waves and their curvature and torsion distributions. This is an interesting scientific question because while vortex filaments are the primary geometric character in quantum fluids, they are ubiquitous in fluids generally, e.g., wing-tip vortices, smoke/bubble rings, decomposition of large-scale vortical flows. Consequently, a greater understanding of these objects has wide-scale utility in fluid systems. Our primary goal is to understand simulations of a particular family of vortex filament flows, e.g., curvature-dependent binormal flows. Important here is the correlation between these predictions and large-scale continuum properties of the fluid system. To do this, we will need to derive connections between this family of flows and important physical distributions so that the simulated results can be extended past their geometric implications.

Grand Challenge: Not applicable

Researcher’s Associated Literature Tree: https://arxiv.org/abs/1803.00147 https://arxiv.org/abs/1712.05885 https://arxiv.org/abs/1102.2258 Additional Information: Unified Non-Local Theory of Transport Processes Generalized Boltzmann Physical Kinetics, Historical Introduction and the Problem Formulation https://www.sciencedirect.com/science/article/pii/B9780444634788099875 254A, Notes 0: Physical derivation of the incompressible Euler and Navier-Stokes equations https://terrytao.wordpress.com/2018/09/03/254a-notes-0-physical-derivation-of-the-incompressible-euler-and-navier-stokes-equations/

Scott Strong