Numerical study of nonlinear resonance in narrow bay

A two-dimensional finite element model is developed to solve Nwogu´s modified Boussinesq equations. The governing equations are rearranged in such a way that it is suitable for using linear unstructured elements. To remove the third order spatial derivative terms in the governing equations, auxiliary variables are introduced. The suitability of the present model for the harbor resonance problem is investigated. An internal wave-maker is implemented over the unstructured mesh and a sponge layer is installed in the open ocean. The performance of the model for the nonlinear response of the rectangular bay is investigated. By comparing the numerical results with Rogers and Mei´s theoretical solutions and experimental data, it is verified that the present model is capable of simulating the amplification of nonlinearly generated super-harmonic component through resonant interaction