It has been a while. I’ve been working on quite a few projects with a few students. I’ve made significant progress on the conservation laws project as well as the time-dependent pressure problem.
Conservation Laws Project
I recently gave a talk on this in the “Waves in One World” Series. You can find a direct link to the talk as well as the corrected slides below. I’ll write more information about this in an upcoming post once we have completed the pre-prints.
Talk Abstract: We consider a nonlocal formulation of the water-wave problem for a free surface with an irrotational flow, and show how the problem can be reduced to a singleequation for the interface. The formulation is also extended to constant vorticity and interfacial flows of different density fluids. We show how this formulationcan be used to systematically derive Olver’s conservation laws not only for an irrotational fluid, but for constant vorticity and interfaces. This framework easily lends itself to computing the related conservation laws for various asymptotic models.Waves in One World – Online Seminar – April 22, 2020
Recording of Talk
Annotated Slides (.pdf)
Time-Dependent Pressure Problem
Along the way with the conservation law problem, we discovered a direct map between the pressure at the bottom and the free-surface variables. I’ll detail more about this soon.