The transformation of a solitary wave on an underwater step is studied analytically and numerically. The theoretical model includes the linear potential description of the wave transformation on a step and the weakly nonlinear theory of long waves based on the Korteweg–de Vries equation for reflected and transmitted waves far from a step. Numerical simulation of solitary wave transformation on ...

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems.

A mathematical model of solitary wave interaction with a pontoon-type rigid floating structure over flat bottom is formulated based on Boussinesq-type equations under weakly nonlinear dispersive waves. Based the higher-order Boussinesq equations, equation derived, and semi-analytical solution obtained using perturbation technique. On other hand, brief descriptions application wave2Foam OceanWav...

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin-Bona-Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed an...

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluid...

Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial viscosity terms studied by Chae (Adv. Math. 203 (2006), 497-513) and the three-dimensional stratified rotating Boussinesq equations studied by Hsia, Ma and W...