多重尺度法在流体动力学中的应用

Application of Multiple Scale Method to the Study of Hydrodynamics

从 Navier- Stokes(N- S)方程和质量守恒方程出发 ,根据潮流、波浪和湍流等时间、空间尺度的不同特点 ,引入摄动理论中的多重尺度法 ,将方程中各物理量分解为与之相关的部分 .在不同尺度下作平均 ,导出不同尺度下波流耦合作用连续方程、动量方程和泥沙方程 ,用数学方法解释潮流波浪间的相互作用和影响 .分别讨论波浪、潮流作用下含沙量的垂向分布 ,与现有理论公式及实测资料进行计算比较 ,得到满意的结果 。

Starting from Navier Stokes equation and equation of conservation of mass,multiple scale method from perturbation theory is drawn into the study of hydrodynamics in line with the characteristics of tidal current,wave,turbulence and other temporal and spatial sacles.By which all the physical quantities in N S equation are decomposed into parts correlated with it and the mean is taken under different scales.A continous equation of wave and tide coupling under different scales and a momentum equation and a silt equation are derived for mathematical explaination and discussion.The interaction and the mutual influence of wave and tide are mathematically explained;and the vertical distribution of sediment concentration under the action of wave and tide is discussed respectively.As compared with theoretical formula and field data now available,the authors′s results are satisfactory.They are conducive to the further study of hydrodynamics and silt transportation.