Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth

• Published in: Journal of hydrodynamics. Series B 2015-06, Vol.27 (3), p.321-331
• Main Author: 王苹 卢东强
• Format: Article
• Language: English
• Subjects: Engineering; Engineering Fluid Dynamics; finite water depth; homotopy analysis method (HAM); Hydrology/Water Resources; nonlinear short-crested waves; Numerical and Computational Physics; Simulation; wave energy; wave profile; 同伦分析; 波浪高度; 波的传播; 流体; 潜在能量; 线性色散关系; 逼近; 非线性波
• ISSN: 1001-6058; 1878-0342
• DOI: 10.1016/S1001-6058(15)60489-9

A nonlinear short-crested wave system, consisting of two progressive waves propagating at an oblique angle to each other in a fluid of finite depth, is investigated by means of an analytical approach named the homotopy analysis method (HAM). Highly convergent series solutions are explicitly derived for the velocity potential and the surface wave elevation. We find that, at every value of water depth, there is little difference between the kinetic energy and the potential energy for nonlinear waves. The nonlinear short-crested waves with a larger angle of incidence always contain the more potential wave energy. With the aid of the HAM, we obtain the dispersion relation for nonlinear short-crested waves. Furthermore, it is shown that the wave elevation tends to be smoothened at the crest and be sharpened at the trough as the water depth increases, and the wave pressure crests and troughs become steeper with increasing incident wave steepness.