Numerical Computation of Steady Rotational Waves and Recovery of the Surface Profile from Bottom Pressure Measurements

This chapter demonstrates how to easily compute rotational gravity waves and solve an inverse problem for the recovery of surface wave profiles from discrete pressure measurements at the seabed. For the first step, we solve the steady Euler equations using a boundary integral method based on the Cauchy integral formula. For the recovery procedure, we reduce the nonlinear equations to an implicit algebraic expression for the free surface and solve it numerically by means of an iterative algorithm. We compare both computed and recovered solutions through a couple of non-trivial numerical examples to illustrate the effectiveness of our approach.