Water-wave profiles from pressure measurements: Extensions

In this letter, we present a method to reconstruct the surface elevation of an inviscid traveling gravity wave in two dimensions using the pressure measured at any depth. In order to achieve this reconstruction, we derive a map from the pressure at an arbitrary depth p(x,z0) to the horizontal velocity at the bottom of the fluid domain. Once this map is established, we use the result presented in Oliveras et al. (2012) to find the free-surface η. In addition to the fully nonlinear relationship, we present a “heuristic” asymptotic formula that does not involve the wave speed c.