Boussinesq-type equations of hydroelastic waves in shallow water

• Published in: Journal of Fluid Mechanics
• Main Authors: Tang, Shanran, Xiong, Yingfen, Zhu, Liangsheng
• Other Authors: National Natural Science Foundation of China
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 2024
• Subjects: Sea ice
• Online Access: http://dx.doi.org/10.1017/jfm.2024.233; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112024002337

Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydroelastic waves, in which non-uniform distribution of structural stiffness and varying water depth are considered rigorously. Application of Boussinesq assumptions enables complicated three-dimensional problems to be reduced and formulated on the two-dimensional horizontal plane, therefore the proposed Boussinesq-type models are straightforward and versatile for a wide range of hydroelastic wave applications. Two configurations, a floating plate and a submerged plate, are studied. The first-order linear governing equations are solved analytically with periodic conditions assuming constant depth and uniform stiffness, and the linear dispersion relations are subsequently derived for both configurations. For flexural-gravity waves of a floating plate, unique behaviours of flexural-gravity waves different from shallow-water waves are discussed, and a generalized solitary wave solution is investigated. A nonlinear numerical solver is developed, and nonlinear flexural-gravity waves are found to have smaller wavelength and celerity than their linear counterparts. For hydroelastic waves of a submerged plate, dual-mode analytical solutions are discovered for the first time. Numerical computation has demonstrated that a plate with decreasing submerged depth is able to transfer wave energy from the deeper water to the surface layer.