In this study, an analytic approach for the complete second-order solution proposed by Sulisz and Hudspeth  was applied to solve a problem of waves propagating over a rectangular submerged structure. In addition, nonlinear wave evolutions above the submerged structure were studied. The nonlinear problem was expressed up to the second-order boundary value problems by using a Taylor series expansion and the perturbation method. In solving the problem, the nonhomogeneous problem was divided into Stokes wave and free wave counterparts. The solutions of neighboring regions were combined and solved by applying kinematic and dynamic matching conditions. Convergence of the presented theory is examined. The experimental results with and without evanescent modes were compared with previous solutions and effects of evanescent modes can be identified. Further comparisons of the presented theory with previous experimental results also indicated favorable consistency. Using the presented theory, the second-order effects of structural submergence, relative water depth, and wave steepness on wave evolutions were investigated. Parametric studies have indicated that shallow water depths above the structure and shallow relative water depth induce high-shoaling second-order waves. In addition, the second-order wave evolution above the structure increased with the wave steepness.
Lee, Jaw-Fang; Tu, Lih-Fu; and Liu, Cheng-Chi
"NONLINEAR WAVE EVOLUTION ABOVE RECTANGULAR SUBMERGED STRUCTURES,"
Journal of Marine Science and Technology: Vol. 22:
5, Article 1.
Available at: https://jmstt.ntou.edu.tw/journal/vol22/iss5/1