Abstract The role of various long-wave approximations in the description of the wave field and bottom pressure caused by surface waves, and their relation to evolution equations are being considered. In the framework of the linear theory, these approximations are being tested on the well-known exact solution for the wave spectral amplitudes and pressure variations. The famous Whitham, Korteweg–de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations have been used as evolutionary equations. It has been shown that if the wave is long, though steep enough, the BBM approximation gives better results than the KdV approximation, and they are quite close to the exact results. The same applies to the description of rogue waves, though formed from smooth relatively long waves, are often short and steep, then they may be invisible in variations of the bottom pressure. Another advantage of the BBM approximation for calculating the bottom pressure is the ability to analyze noisy series without preliminary filtering, which is necessary when using the KdV approximation.

中文翻译：

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底压描述中的长波近似

摘要 各种长波近似在描述面波引起的波场和底压方面的作用，以及它们与演化方程的关系正在被考虑。在线性理论的框架内，这些近似值正在众所周知的波谱振幅和压力变化的精确解上进行测试。著名的 Whitham、Korteweg-de Vries (KdV) 和 Benjamin-Bona-Mahony (BBM) 方程已被用作进化方程。已经表明，如果波很长，尽管足够陡峭，BBM 近似比 KdV 近似给出更好的结果，并且它们非常接近精确结果。这同样适用于对流氓波的描述，尽管由相对较长的平滑波形成，但通常又短又陡，那么它们在底部压力的变化中可能是不可见的。BBM 近似计算底部压力的另一个优点是无需初步过滤即可分析噪声序列的能力，这在使用 KdV 近似时是必要的。