A numerical method is proposed for computation of large amplitude water waves interacting with depth varying currents. The proposed method is developed for fixed mean-depth of water for which a theoretical formulation has recently been introduced in the literature Henry (2013b, 2013c) but no numerical studies have been performed yet. The proposed method relies on a numerical continuation approach for computing large amplitude waves bifurcating from the steady laminar flows. This study hence is on the numerical continuation method for computing two-dimensional (2D) large-amplitude steady water waves on rotational flow with an arbitrary current profile, based on an emerging formulation of the problem. For given mean water depth, current profile, and wave length, the method is able to generate a group of waves from the laminar flow solution to the limiting wave of the largest wave height. Due to the normalization effect in the formulation, the computational domain is fixed regardless of the wave length and water depth, allowing for efficient computation even when dealing with long waves in deep water. The method is first applied to study non-linear wave-current interactions in ocean engineering demonstrating its potential in capturing the wave period changes with increasing wave amplitude in the presence of current. Furthermore, wave characteristics are investigated for cases of constant and discontinuous vorticity, revealing some interesting features. In particular, for waves on linear shear flows, the surface profiles of the waves with the largest amplitude for a range of the vorticity values tend to pass through two fixed points in the 2D plane, and this characteristic seems to be invariant of the water depth.

提出了一种数值方法，用于计算与深度变化的电流相互作用的大振幅水波。提出的方法是为固定的平均水深开发的，最近在文献Henry（2013b，2013c）中引入了理论公式，但尚未进行数值研究。所提出的方法依赖于数值连续方法来计算从稳定层流分叉的大振幅波。因此，这项研究是基于一种新出现的问题，它是一种数值连续方法，用于在具有任意电流分布的旋转流上计算二维（2D）大振幅稳定水波。对于给定的平均水深，电流分布和波长，该方法能够从层流解到最大波高的极限波产生一组波。由于配方中的归一化效果，计算域是固定的，与波长和水深无关，即使在深水中处理长波时也可以进行有效的计算。该方法首先用于研究海洋工程中的非线性波浪-电流相互作用，证明了其在捕获波浪的情况下捕获波浪周期变化的潜力，该变化在存在电流的情况下随波浪幅度的增加而变化。此外，研究了恒定涡旋和不连续涡旋情况下的波浪特征，揭示了一些有趣的特征。特别是对于线性剪切流中的波浪，