Background

Experiments with circular hydraulic jumps in viscous fluids have revealed the existence of quasi-steady states in which the hydraulic jump takes a nearly-polygonal shape:

• https://iopscience.iop.org/article/10.1088/0951-7715/12/1/001/meta
• https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.036316

Understanding of the mechanism behind this is still incomplete. It is generally believed that viscosity, vorticity, and surface tension all play important roles.

Somewhat surprisingly, preliminary numerical experiments with the shallow water equations with an added viscosity term have also exhibited nearly-polygonal hydraulic jumps.

Plan

• Implement viscosity in the shallow water equations in Clawpack
• Try to reproduce earlier FEM experiments showing polygonal jumps
• Possibly use IMEX time integration for efficiency

Nature of project

This project involves a lot of programming and running computational experiments. If the experiments are successful, a possible further part of the project could involve stability analysis of the shallow water equations.