Various Research Threads

Conservation Laws

Using the AFM formulation, I am working to

  1. easily write down the conservation laws as outlined in Olver’s 1982,1983 work, and
  2. use these equations to formulate various “hydrodynamic” hierarchies of equations.

Blog posts related to progress on this project can be found by following the Conservation Law tag

Multiple Scales & Model Reductions

As the conservation law project continues to evolve, one of the questions about model reduction has spawned a new line of research problems. Here, the ultimate goal is to identify model scales using field data via an optimization process. Details and blog posts related to this topic can be found by following the Multiple Scales tag.

Vorticity

In a joint project with Vishal Vasan and Patrick Sprenger, we are considering the stability of traveling wave solutions in the presence of constant vorticity.  Details and blog posts can be found by following the Constant Vorticity tag.

Pressure Relationships

Building on the joint work with Vishal Vasan, Bernard Deconinck, and Diane Henderson, I’m still looking at various relationships between the pressure and the free-surface elevation.  Details and blog posts related to this topic can be found by following the Pressure tag.