On Wave Field Reconstruction Based on a Single Probe Data in Long Crest Waves

Abstract

The time history of wave elevations measured at a single wave probe in long crest waves is used to reconstruct the propagating wave field. The reconstruction follows the potential flow theory with linear or nonlinear free surface boundary conditions. The linear approach is used to verify the relation between the sample size of the probe data and the size of the valid reconstruction zone. It is also used to prescribe the initial conditions of the reconstructed wave system on a 2D spatial domain in terms of the free surface elevation and the velocity potential at calm water surface z=0 and t=0. The nonlinear approach is based on a HighOrder-Spectral (HOS) method which takes the initial conditions generated by the linear approach and propagates the wave system in time and space in a linear or nonlinear fashion. The numerically reconstructed waves using both approaches are compared with the measured waves at location(s) of (a) a single probe and (b) multiple probes aligned with the direction of the wave propagation. The relation between the probe location and the reconstruction point is investigated. The difference between the linear and the nonlinear approach up to the 3rd order is also investigated. The results show that for a wave system with moderate spectral steepness (Hs/λm= 0.03), the wave elevation calculated at a point within the valid reconstruction zone by either the linear wave theory or the 1st order HOS method matches well with the measurement.