应用多重尺度法推导浅水波方程和悬沙扩散方程

根据潮流、波浪及湍流运动尺度不同的特点，引入奇异摄动理论中的多重尺度法，应用导数展开法分离Navier-Stokes方程和质量传输方程，导出了波浪作用下的浅水环流方程、潮位和潮流作用下的浅水波方程及波流联合作用下的悬水扩散方程，用数学方法解释了潮流波浪的相互作用和影响。并与雷诺方程进行了比较。为研究海岸动力因素运动规律和诸动力因素与海岸相互作用奠定了理论基础。

Derivations of shallow water wave equations and suspended sediment diffusion equationsby method of multiple scales

Based on the different characteristics of tidal current, wave and turbulence scales, this paper introduces the method of multiple scales in singular perturbation theory, applies the derivative expansion method to separate Narvier-Stokes equation and mass transmission equation, derives the shallow water current equations under the action of waves, the shallow water wave equations under the joint action of tidal level and current and the suspended sediment diffusion equation under the interaction of waves and tide currents. And the interaction and influence of the tidal current and wave were interpreted by means of the mathematical methodology. And the comparison was made with the Reynolds equation. This method lays a theoreticay foundation for researching both the coastal dynamic factors and the interactions of the factors in coastal zone.