应用多重尺度法推导浅水波方程和悬沙扩散方程  

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

作　　者：朱志夏[1] 韩其为[2] 丁平兴[3] 

机构地区：[1]上海交通大学船舶与与海洋工程学院,上海200030 [2]中国水利水电科学研究院,北京100044 [3]华东师范大学河口海岸国家重点实验室,上海200062

出　　处：《水动力学研究与进展（A辑）》2001年第3期279-294,共16页Chinese Journal of Hydrodynamics

基　　金：国家杰出青年科学基金资助项目 (4 982 5 161);华东师范大学河口海岸国家重点实验室资助项目

摘　　要：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沙扩散方程 ,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。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.

关 键 词：多重尺度法 质量传输方程 波流联合作用 浅水波方程 悬沙扩散方程 

分 类 号：O353.2[理学—流体力学]