His research has concentrated especially in the areas of hydrodynamics and free boundary problems. Free Surface Hydrodynamics Wakes behind a ship, waves on a beach, underwater bubbles, jets, sprays, and tsunamis are all examples of free-surface hydrodynamics. We explain how all these phenomena come out of simple requirements of conservation of mass and momentum and a limit to how much water can occupy any volume. A videotape shows some experimental and computed free surfaces. It's one in which an important boundary, such as the boundary between the liquid and solid states of a substance, is one of the unknowns of the problem.
Examples are shock waves, water surfaces, combustion fronts, optimal surfaces, etc.
We describe and illustrate examples in which the free boundaries are very regular and others where their structure becomes very complex. We show how they may be computed for a number of problems. We describe a program which had students working on real applied mathematics research problems provided by a Navy laboratory. We show some of the results obtained. We discuss how similar programs might be devised to fit the needs of different student bodies.