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Equations relating the pressure at a horizontal seabed, the free-surfaceprofile and the surface-pressure are derived for two-dimensional irrotationalsteady water waves with arbitrary pressure at the free surface. Special casesinclude gravity, capillary, flexural and wind waves. Without approximations, weshow that the free-surface recovery from the bottom-pressure requires theresolution of only one first-order ordinary differential equation independentof the surface-pressure, thus providing a new general recovery method valid fora broad class of water waves. Another equation provides an explicit expressionfor the surface-pressure as a function of the bottom-pressure and of thefree-surface. Thus, if unknown, the surface-pressure can be also recovered ifone extra measurement is available. This new recovery procedure is illustratedanalytically for the linear approximation of a flexural-capillary-gravity wave,and numerically for fully nonlinear capillary-gravity waves.

Steady water-waves with arbitrary surface-pressure: Their recovery from bottom-pressure measurements