The deformation of steep surface waves on water - I. A numerical method of computation
The deformation of steep surface waves on water - I. A numerical method of computation
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DOI：
10.1098/rspa.1976.0092
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发表时间：
1976-07
期刊：
影响因子：
--
通讯作者：
M. Longuet-Higgins;E. Cokelet
中科院分区：
文献类型：
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作者：
M. Longuet-Higgins;E. Cokelet
俯冲式断路器超出了所有已知的分析近似值。以前的数值计算只成功地积分了运动方程，直到表面变得垂直的那一刻。本文提出了一种跟踪空间周期无旋表面波时程的新方法。唯一的自变量是自由表面标记粒子的坐标和速度势。在每个时间步长，求出新的速度法向分量的积分方程解。该方法比以往的基于二维网格的方法具有更快、更准确的特点。它还有一个优点，那就是标记的粒子集中在曲率尖锐的区域附近。粘度和表面张力都被忽略。该方法在有限振幅的自由定常波上进行了试验，并与基于Stokes级数的独立计算结果吻合良好。然后将其应用于非定常波，该非定常波最初是通过对对称的行进波施加非对称压力分布而产生的。自由奔腾的海浪随后变陡并倾覆。结果表明，在倾覆发生后的很长一段时间内，表面一直是圆形的。
Plunging breakers are beyond the reach of all known analytical approximations. Previous numerical computations have succeeded only in integrating the equations of motion up to the instant when the surface becomes vertical. In this paper we present a new method for following the time-history of space-periodic irrotational surface waves. The only independent variables are the coordinates and velocity potential of marked particles at the free surface. At each time-step an integral equation is solved for the new normal component of velocity. The method is faster and more accurate than previous methods based on a two dimensional grid. It has also the advantage that the marked particles become concentrated near regions of sharp curvature. Viscosity and surface tension are both neglected. The method is tested on a free, steady wave of finite amplitude, and is found to give excellent agreement with independent calculations based on Stokes’s series. It is then applied to unsteady waves, produced by initially applying an asymmetric distribution of pressure to a symmetric, progressive wave. The freely running wave then steepens and overturns. It is demonstrated that the surface remains rounded till well after the overturning takes place.