New exact relations for easy recovery of steady wave profiles from bottom pressure measurements

Abstract

AbstractThis paper is about the determination of a free surface wave profile from a given pressure distribution at the bottom. For a two-dimensional irrotational steady surface water wave propagating over a flat horizontal bed, this problem is solved analytically in an implicit form. Explicit solutions can be easily obtained numerically via fixed point iterations, whose convergence is outlined mathematically and numerically. This new surface reconstruction procedure does not involve the resolution of a differential or an integral equation, i.e. the surface is given by algebraic local relations. Thus, this formulation permits the free surface recovery in a simpler and more efficient way than previous methods.