ABSTRACT This study aims to develop a new wave equation model by modifying the Fully-nonlinear and strongly-Dispersive Surface wave (FDS) equations. The modification was performed by applying a new expansion in a series of the vertical coordinate, zμ , to the velocity potential while a simple expansion in a series of z was applied to the FDS equations. Verification of the model was conducted by comparing with the theoretical solutions of surface solitary waves. We applied the modified FDS equations to wave fields over a bump under conditions with and without currents, which agreed very well with the time series of wave heights and velocity obtained from laboratory experiments. The dispersion relationship computed using the normalized modified FDS equations also agreed very well with the theoretical solution when we gave the number of expansion terms as 3 with μ = 2.5. Additionally, the profile of surface waves computed with the modified FDS equation was shown to have a larger width ridge, a bulbous-type wave, by comparing with a Trochoidal wave under the condition of waves against a current.

中文翻译：

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凸块上自由表面流动的非线性波动方程

摘要 本研究旨在通过修改完全非线性和强色散表面波 (FDS) 方程来开发新的波动方程模型。修改是通过将一系列垂直坐标 zμ 中的新扩展应用于速度势，同时将一系列 z 中的简单扩展应用于 FDS 方程。通过与表面孤立波的理论解进行比较，对模型进行了验证。我们将修改后的 FDS 方程应用于有和无电流条件下凸起上的波场，这与从实验室实验获得的波高和速度的时间序列非常吻合。当我们将扩展项的数量设为 3 且 μ = 2.5 时，使用归一化的修正 FDS 方程计算的色散关系也与理论解非常吻合。此外，在波浪逆流条件下，与次摆线波相比，用修正的 FDS 方程计算的表面波轮廓显示具有更大宽度的脊，即球根型波。