Numerical Simulations Of Coastal Waves, Wave-induced Currents And The Transport Of Pollutants In Waves And Currents

The shallow coastal zone is extremely dynamic region, where the hydrodynamics are complicated as evident in refraction, diffraction, shoaling and breaking of water waves, as well as the presence of near-shore wave-induced currents, and these hydrodynamic factors influence the coastal pollutant transport remarkably. It is very crucial to study and master the rules of pollutant transport for protecting and renovating the coastal environment. In this paper, based on the dynamic background of coastal waves and near-shore currents induced by the breaking waves, the waves transformation are numerically simulated by the parabolic mild slope equation where the wave reflection effect in dominant direction is ignored, the near-shore wave-induced currents are numerically simulated by the near-shore wave-induced current model coupling the wave numerical results, furthermore, the rules of pollutant transport are studied based on the wave and near-shore wave-induced currents numerical results.In this paper, the wave transformation in several physical experiments are simulated by the parabolic mild slope equation firstly, and long-shore currents formed by the breaking of oblique incident waves in these experiments are also simulated based on the near-shore wave-induced current model coupling the wave numerical results. Subsequently, the coupling numerical models are applied to simulate the wave transformation and wave-induced long-shore currents at Leadbetter Beach, Santa Barbara, USA. The distribution characteristics of wave transformation and wave-induced long-shore currents in this coastal zone are studied, and the numerical results have been well validated by field data, which indicats the applicability and validity of the coupling numerical models for the waves and near-shore wave-induced current numerical simulation based on the theory of regular wave in practical coastal zone.In coastal zones, the hydrodynamics are very complicated, the wave transformation is not regular or repetitive, and the waves exist as irregular waves or random waves. In this paper, the irregular wave transformation in several physical experiments are simulated by the parabolic mild slope equation based on the theory of linear superposition, and the long-shore currents formed by the breaking of oblique incident irregular waves are simulated based on the near-shore wave-induced current model coupling the irregular wave numerical results. Subsequently, the coupling numerical models are applied to simulate the random wave transformation and wave-induced long-shore currents at Leadbetter Beach, Santa Barbara, USA. The distribution characteristics of random wave transformation and wave-induced long-shore currents in this coastal zone are studied, and the numerical results have been well validated by field data, which indicats the applicability and validity of the coupling numerical models for the waves and wave-induced near-shore currents numerical simulation based on the theory of random wave in practical coastal zone.Since the topography and coastline in the coastal zones are generally complicated, the conventional numerical modeling in Cartesian coordinates system based on the rectangular grids may easily lead to the state that computational domain boundary does not match with the actual border, and the accuracy of numerical result is reduced. Some merits make the curvilinear coordinates transformation as an outstanding mathematical method to deal with complex boundary in fluid dynamics. Firstly, the boundary-fitted grids can achieve a seamless fit to the curve border; secondly, the size of the grids can be adjusted according to changes in topography; and lastly the coordinate transformation will not change the numerical method in most cases. For achieving the numerial modeling of shallow water waves and wave-induced currents in coastal zones with complex terrain and variable boundarie, the wave transformation model in the orthogonal curvilinear coordinates is set up based on the curvilinear parabolic approximation mild slope equation combining with the orthogonal curvilinear grid system. Coupling the wave transform model, the wave-current model in the orthogonal curvilinear coordinates is set up based on the concept of radiation stress as a driving force under the same orthogonal curvilinear grid system used in the wave transformation model. The wave-induced currents in some cases with complex terrain and variable boundarie are numerically studied based the coupling models very well.The pollutant transport is remarkably affected by the coastal hydrodynamics. Based on the hydrodynamics of coastal waves and near-shore wave-induced currents, the pollutant transport model in the orthogonal curvilinear coordinates is set up. The coupling three models including wave transform, near-shore wave-current and pollutant transport are applied to numerically model pollutant transport under the coaction of waves and currents in several physical experiments or the practical coastal zone, and the rules of pollutant transport are studied.