A method to recover water-wave profiles from pressure measurements

• Published in: Wave motion 2017-12, Vol.75, p.25-35
• Main Authors: Vasan, Vishal, Oliveras, Katie, Henderson, Diane, Deconinck, Bernard
• Format: Article
• Language: English
• Subjects: Cnoidal waves; Displacement; Measurement; Pressure; Pressure measurement; Recovery; Time series; Transfer functions; Water waves
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2017.08.003

An operational formulation is proposed for reconstructing a time series of water surface displacement from waves using measurements of pressure. The approach is based on the fully nonlinear formulation for pressure below traveling-wave solutions of Euler’s equations developed by Oliveras, Vasan, Deconinck and Henderson. Its validity is tested using experiments in which both the pressure and the surface displacement are measured. The experiments include a wave system that is Galilean invariant – cnoidal waves, and wave systems that are not – reflected cnoidal waves and wave groups. We find that since the proposed formulation is nonlinear, it reproduces the amplitude spectrum of the measured surface displacements better than the hydrostatic model and better than the linear model that takes into account the pressure response factor due to small amplitude waves (the transfer function). Both the proposed formula and the transfer function reconstruct the surface reasonably well, with the proposed formula’s being about 5% more accurate. •We propose a method to recover surface elevation profiles from pressure measurements.•It is more accurate than traditional means for nonlinear traveling waves.•It is as computationally efficient as linear theory.•Experimental comparisons show the method works for interacting waves and wave groups.