A Numerical Model Of Nearshore Wave Field

As waves proceed from offshore to near shore regions, their characters such as wave celerity, length, wave height, pressure field et al. will change to some degree. The effects of wave transformation, refraction, diffraction, reflection and breaking are all due to the varying topography, bottom friction, obstacles (buildings, islands, capes, shoals, banks), current, local current climate. It is an effective and feasible way to simulate the wave transformation in mathematical ways in real coastal engineering. A new mild slope equation is developed based on the classical linear theory of water waves to describe the wave transformation process, including both refraction and diffraction, from deep through shallow water in terms of the velocity potential function.The computational effort involved and computer memory requirements restrict the applicability of the model for real case application, at least for the present generation of computer hardware. In this paper Green's formula and the Lagrangian formulation are both adopted respectively to derive two hyperbolic equations including higher-order bottom effect, and the results show that these two equations are identical. In addition, terms of bottom friction and nonlinear factor are added into. The boundary conditions for the present model are the same as those used in the elliptic model. Following Mei (1983), the slow coordinate for the time variable is introduced. A new time dependent mild slope equation to be act as the governing equation in this paper is obtained after a lengthy algebraic manipulation. The well known Alternating Direction Implicit (ADI) method is used to solve the mentioned equation. A relaxation factor (Pan,1999) is employed to accelerate the convergent speed comparatively.The effect of the nonlinear dispersion relationship and the rapidly varying topography will be verified in the fourth section. When it is evaluated, the nonlinear term (Kirby&Dalrymplel987) will be introduced, other nonlinear ones are also will be used to make a comparison. The squared bottom slope and the bottom curvature included in the topography term will be calculated and analyzed respectively. The model based on the equation has been applied to the expansion project of some harbor successfully. It can simulate wave refraction, diffraction and reflection on breakwater efficiently. Comparison of the wave climate including wave height, direction and length against other model results has been made and good agreement has been achieved. So the mild-slope equation model can be applied to simulate waves incoastal engineering and the extended terms also can be taken into account if necessary.