Project Info

Geometric Quantum Hydrodynamics: Modeling and Simulation of Vortex Rings in Ideal Fluids

Scott Strong | sstrong@mines.edu

Vortex lines are stable structures fundamental to energy and mass transport in a variety of fluid phenomenon. While the contexts in which they appear are often complicated, e.g., quantum fluids, much of their mathematics is accessible to Mines undergraduates who have completed our core curriculum. In particular, a motivated undergraduate student who is proficient in core mathematics and physics can make a significant contribution to a project whose goal is to model and simulate vortex motion in an effort to advance our understanding of the relationship between energy transfer mechanisms and helical modes of vortex lines. Such questions must be addressed if we are to understand the relaxation of turbulent structures even in the absence of fluid viscosity, the typical agent of energy dissipation in fluid systems.

The goals of this project are:

1. Through a structured mentoring program, prepare the Mines undergraduate student for academic research.

2. Understand the mathematical modeling of fluid systems, and analysis of specific systems defined by vorticity constrained to exist on approximately one-dimensional subregions.

3. Characterize the relationship between highly localized curvature structures on vortex rings and their decomposition into helical modes.

More Information

Seminal results:

Hasimoto, A soliton on a vortex filament (1972) DOI: https://doi.org/10.1017/S0022112072002307

Ricca, Rediscovery of Da Rios equations (1991): https://www.nature.com/articles/352561a0

Textbook Information:

https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law
https://en.wikipedia.org/wiki/Frenet%E2%80%93Serret_formulas

Researcher’s Associated Literature Tree:

https://arxiv.org/abs/1803.00147
https://arxiv.org/abs/1712.05885
https://arxiv.org/abs/1102.2258

Grand Engineering Challenge: Not applicable