Vortex Theory for Two Dimensional Boussinesq Equations

In this paper, the single center vortex method (SCVM) is extended to find some vortex solutions of finite core size for dissipative 2D Boussinesq equations. Solutions are expanded in to series of Hermite eigenfunctions. After confirmation the convergence of series of the solution, we show that, by considering the effect of temperature on the evolution of the vortex for the same initial condition as in [19] the symmetry of the vortex destroyed rapidly.

Numerical model for simulation of waves in surfzone and nearshore areas based on Boussinesq equations: results for plane beaches

A numerical model based on the 2D Boussinesq equations has been developed using the Finite Volume Method. The model was verified against experimental data for the case of wave breaking on a sloping beach. Simulated results by the model showed that the model has good capability of simulation of waves in the nearshore area. Numerical simulation was also carried out for the problem of waves on a plane beach with a breakwater and submerged dunes. Simulated results were compared with those computed by MIKE 21. The comparison showed that good agreements were obtained and confirmed the applicability of the Boussinesq model to the simulation of physical phenomena of waves in the nearshore areas, especially, suitable for the simulation of wave-induced current including rip currents.