Measuring Water Waves: Using Pressure to Reconstruct Wave Profiles

Document Type

Presentation Abstract

Presentation Date

11-8-2021

Abstract

How does one measure waves in the ocean? And how accurate are these methods at capturing the height and shape of the wave? In this talk, I will discuss an inverse problem related to measuring water-waves using pressure sensors placed inside the fluid. We will begin by introducing the partial differential equations that describe fluid motion. Then, using a non-local formulation of the water-wave problem, we will see how to 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.

Additional Details

November 8, 2021 at 3:00 p.m. in Math 305

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