The software code on mathematical derivation from The theory of fifth-order Stokes waves in a linear shear current

In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by using the perturbation method originally proposed for pure waves that was recently published. The present solutions are checked against the existing experimental data, the third-order stream function solutions, as well as the numerical results. The comparisons demonstrate that the present solutions are more accurate in describing the velocity distributions during wave propagation, especially in strong following currents and negative vorticity conditions. Subsequently, the present solutions are used to investigate the fluid particle trajectories for different wave–current interaction conditions. The results indicate that the background vorticity can alter the patterns of fluid particle trajectories and the direction of Stokes drifts.

本研究采用近期发表的、最初针对纯波浪提出的摄动法，推导得到一组全新的含线性剪切流效应的五阶斯托克斯（Stokes）波浪解。将本次推导的解与已有实验数据、三阶流函数解及数值计算结果进行对比验证，结果表明，本研究所获解在描述波浪传播过程中的流速分布时精度更优，尤其在强顺流与负涡量工况下表现更为突出。随后，利用该五阶斯托克斯波浪解，针对不同波流相互作用工况开展流体质点运动轨迹的研究，结果显示背景涡量能够改变流体质点的运动轨迹形态与斯托克斯漂移方向。