摘要
Using the linear wave theory, the distributions of the wave induced excess momentum fluxes over depth at the arbitrary wave angle and their asymptotic forms for deep and shallow water are developed. Results indicate that the distribution of the wave induced excess momentum fluxes over depth is non uniform and the contributions of the component below the wave trough to the total momentum fluxes become considerable in shallow water. On the basis of the Navier Stokes equations, the simplified three dimensional mathematical model is established by taking a phase average over a wavelength. It is found that there are the terms of the wave induced excess momentum fluxes varying over depth in the model, which illustrates the situation of wave current interactions and the vertical structure of current velocity are changed because of different wave induced excess momentum fluxes at various vertical location. The finite difference method is employed to solve the simplified model. Performances of the two dimensional vertically integrated equations are evaluated against available numerical and experimental results including the cases of wave set up on a plane beach, longshore current due to an oblique wave, wave induced nearshore circulation in a semi enclosed seas, and wave current interactions. All cases yield satisfactory agreements. The three dimensional mathematical model is applied to the numerical simulation of wave current interactions, and it performs well in predicting the vertical velocity structure and the plane flow field.
Using the linear wave theory, the distributions of the wave induced excess momentum fluxes over depth at the arbitrary wave angle and their asymptotic forms for deep and shallow water are developed. Results indicate that the distribution of the wave induced excess momentum fluxes over depth is non uniform and the contributions of the component below the wave trough to the total momentum fluxes become considerable in shallow water. On the basis of the Navier Stokes equations, the simplified three dimensional mathematical model is established by taking a phase average over a wavelength. It is found that there are the terms of the wave induced excess momentum fluxes varying over depth in the model, which illustrates the situation of wave current interactions and the vertical structure of current velocity are changed because of different wave induced excess momentum fluxes at various vertical location. The finite difference method is employed to solve the simplified model. Performances of the two dimensional vertically integrated equations are evaluated against available numerical and experimental results including the cases of wave set up on a plane beach, longshore current due to an oblique wave, wave induced nearshore circulation in a semi enclosed seas, and wave current interactions. All cases yield satisfactory agreements. The three dimensional mathematical model is applied to the numerical simulation of wave current interactions, and it performs well in predicting the vertical velocity structure and the plane flow field.
