The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: Measuring Water Waves: Using Pressure to Reconstruct Wave Profiles
Abstract: Euler's equations describe water-waves on the surface of an ideal fluid. In this talk, I will discuss an inverse problem related to measuring water-waves using pressure sensors placed inside the fluid. Using a non-local formulation of the water-wave problem, we can directly determine the pressure below both traveling-wave and time-dependent solutions of Euler's equations. This method requires the numerical solution of a nonlinear, nonlocal equation relating the pressure and the surface elevation which is obtained without approximation. From this formulation, a variety of different asymptotic formulas are derived and are compared with both numerical data and physical experiments.