Mild Slope Equation Considering The High Order Effect And Its Application

As surface waves propagate from deep to shallow water, the nonlinear will strengthen, due to the effect of topography and various hydraulic structures. Weak nonlinear dispersion can't be used to describe the powerful nonlinear of water wave.In this paper, based on summarizing previous numerical studies on wave transformations, deriving an extended form of mild slope equation, which is taken as the governing equation. The equation simulates wave transformation in offshore area with finite difference.Based on the Laplace equation, reviewing the process of deducing the traditional mild slope equation and Maa's equation by using perturbation method. On the foundation of Maa's mild slope equation, an extended form of mild slope equation which considers the effect of slope, bottom friction and wave breaking is derived.There is an undetermined coefficient C, in the mild slope equation considering the effect of high-order term, which is assumed as a constant. Analysing non-linearity of the improved mild slope equation by adjusting the value of C₁.In order to verify the applicability and accuracy, the model is tested by computing wave field for several classical examples of laboratory experiments.Compared simulation results with measured data, to confirm optimal value of C₁ forthe different experiment topography. Validated by experiment data and numerical simulation result of the mild slop equation which developed by Maa et al. the extended model of mild-slop equation can give more accurate computed results thanthe Maa's mild slop model. The unity, related function, physical significance of C₁should be researched and discussed in further.Finally,using the extended form of mild slope equation numerical model to simulate waves in the practice topography. The simulated results agree with the locate situation well, which illustrated that the extended numerical model is applied to the wave transformation in the practical complex topography.