Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include gravity, capillary, flexural and wind waves. Without approximations, we show that the free-surface recovery from the bottom pressure requires the resolution of only one first-order ordinary differential equation independent of the surface pressure, thus providing a new general recovery method valid for a broad class of water waves. Another equation provides an explicit expression for the surface pressure as a function of the bottom pressure and of the free surface. Thus, if unknown, the surface pressure can also be recovered if one extra measurement is available. This new recovery procedure is illustrated analytically for the linear approximation of a flexural–capillary–gravity wave, and numerically for fully nonlinear capillary–gravity waves.

中文翻译：

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具有任意表面压力的稳定水波：从底部压力测量中恢复

对于自由表面任意压力的二维无旋稳定水波，导出了水平海床压力、自由表面剖面和表面压力的方程。特殊情况包括重力波、毛细管波、弯曲波和风波。在没有近似的情况下，我们表明从底部压力进行自由表面恢复只需要求解一个与表面压力无关的一阶常微分方程，从而提供了一种适用于广泛类型水波的新的通用恢复方法。另一个方程提供了表面压力作为底部压力和自由表面的函数的显式表达式。因此，如果未知，如果有一项额外的测量可用，也可以恢复表面压力。这种新的恢复程序对弯曲毛细管重力波的线性近似进行了分析说明，并对完全非线性毛细管重力波进行了数值分析。