中文摘要：

从Laplace方程和非线性的边界条件出发，通过将波动速度势函数表达为任意特定水深处的函数，推导了线性频散关系具有Airy波精确解的Pad6[2，2]阶近似精度的高阶非线性Boussinesq型方程。方程含有能量耗散项并完全满足水底边界条件。定性比较了高阶非线性方程和弱非线性方程的非线性特征。推导了二维四阶的滤波公式。建立了非线性波传播的数值模拟模型。结合两个具体算例，比较了数值模拟模型的强非线性版本和弱非线性版本的计算结果之间的差别，从而定量探讨了高阶非线性项对数值计算结果的影响。

英文摘要：

With the wave velocity potential function being expressed as a function defined at an arbitrary water level, a set of high-order nonlinear Boussinesq-type equations is derived from the Laplace equation and the nonlinear boundary conditions. The derived set of equations is accurate up to [2, 2] pad6 approximation in linear dispersion, includes the dissipative terms and fully satisfies the sea bottom boundary condition. The nonlinear characteristic is compared between the present high order nonlinear equations and the weakly nonlinear ones. The two-dimension fourth order filter formula is also provided in this paper.The numerical model for wave propagation is described. With two test cases numerically high order nonlinear version of the numerical model are compared to those of the weakly the effects of high order nonlinear terms on wave propagation are studied quantitatively. simulated, the modeled results of the nonlinear version. This indicates that