Research On The Rotational Motion Caused By Wave Breaking

Wave breaking is a common phenomenon in nature and engineering practice. Since the nonlinear and dispersion properties of Boussinesq equation are improved and the solving method is mature, Boussinesq models can handle most of wave phenomena (propagation, shoaling, breaking and wave-mean flow interaction) and they are widely used in the nearshore. So how to extend the range of Boussinesq equation applications into the surf zone is a hot and difficulty, which plays an important role not only in theoretical significance, but also in engineering significance.Scholars, at home or abroad, have done a lot of research on wave breaking on the base of Boussinesq equations, which give us much precious literature and also lay the foundation for our further research work. Briganti solved the vorticity transport equation with the equations containing vorticity which is proposed by Veeramony and Svendsen to solve the problem of wave breaking, and analyzed the results by means of four different profiles of eddy viscosity.Based on the Briganti’s Boussinesq equation of wave breaking model, this paper considers the rotational motion when dealing with the problem of wave breaking. The governing equation is two-parameter Boussinesq equation and it is compared with the governing equation in consideration of the rotational motion proposed by Da Shan, and find out the breaking terms caused by the rotational motion in his momentum equation. Assuming that the eddy viscosity is a uniform distribution along the water depth, and using the boundary conditions of vorticity obtained by fitting to hydraulic jump experiment of Veeramony and Svendsen, vorticity transport equation is solved to determine the distribution of vorticity. Rotational velocity is calculated by the distribution of vorticity and add the breaking terms caused by the rotational velocity into the two-parameter Boussinesq equation. The numerical model is solved by the finite difference method of ABM on staggered grid system and analyze the properties of the vorticity and rotational motion caused by the wave breaking. The numerical model in this paper is used to simulate wave breaking on a uniform plane beach, and the numerical results obtained by the numerical model in this paper are compared with available experimental and numerical data and they are in a good agreement, which proves the availability of the present wave breaking model and efficiency of the numerical method in this paper.