Numerical Simulations Of The Mild Slope Equations For Coastal Waves And Studies On The Transport Of Pollutants In Waves And Currents

Coastal and offshore areas are extremely dynamic regions, where the advection and diffusion of pollutants are more complex because of the complicated wave field, such as the distortion and breaking of water waves. The rules of the pollutants transport due to the coastal hydrodynamics should be studied to protect and improve the sea environment. In this paper, based on the wave-current field which is induced by the breaking waves as wave propagating to the coastal zone, the mild slope equations of waves, wave-current model, and pollutants transport in the near-shore region in waves and currents have been numerically simulated, and the rules of the pollutants transport have been studied by experiment.In the paper, three kinds of mathematical models for the propagation and transformation of waves: elliptic mild slope equation, parabolic mild slope equation and hyperbolic mild slope equation have been numerically simulated. The elliptic mild slope equation takes the reflection, refraction and diffraction effect of water waves into account, and the linear and nonlinear dispersion relations of waves have been used respectively in the numerical simulating elliptic mild slope equation, and the numerical results have been validated in the paper; in view of the lower efficiency in numerical simulating elliptic mild slope equation, a flexible and effective numerical method has been successfully applied to the numerical simulating elliptic mild slope equation, and the calculation efficiency of the elliptic mild slope equation has been improved.The parabolic mild slope equations have been used efficiently in numerical simulating the wave field if only the forward wave propagation is considered. In the paper, the low-level parabolic mild slope equation used for the little incident angle wave propagation, the mini-max principle parabolic mild slope equation and Li's parabolic mild slope equation used for the larger incident angle wave propagation, have been numerically simulated and the numerical results have been studied and compared.The hyperbolic mild slope equation can be numerically simulated more efficiently than the elliptic mild slope equation, and the backward wave propagation has been considered in the hyperbolic mild slope equation. In this paper, two kinds hyperbolic mild...