关于不同尺度大气运动中的雷诺交换

本文从多尺度分解概念出发,建立了多尺度Reynolds方程组。证明了平均运动的Reynolds交换项应为各级子平均运动非线性项的平均和。文中将子尺度运动处理为描述质点个别运动的Langevin形式以避免Euler方式导致的高阶闭合困难,简单地得到了K闭合表示,给出了动量、热量、质点交换系数的表达式并阐明了它们之间差异的形成原因。此外本文还给出了表现无序脉动量在导向力(如浮力、科氏力)作用下建立有序平均量梯度的负K值及其存在条件,解释了大气中大尺度运动的一些负粘性现象。

ON THE REYNOLDS EXCHANGE IN THE ATMOSPHERIC MULTI-SCALE MOTIONS

In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the concept of decomposing the meteorological elements into multi-scale disturbances. It is proved to be true that the Reynolds exchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions. In order to avoid the higher order closure in Eulerian approaches, a new K-theory based on the multi-scaled Reynolds equations is given in which the subscale motions are described by Langevin equation as the air particales are moving in the Eulerian average background. From the new K-theory are derived the momentum, heat and mass exchange coefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity, temperature and other meteorological elements in disturbances. The new K-theory also expounds the causes that lead to the differences between the exchange coefficients of one element and another and give the ambient conditions in which the buoyancy and/or Coriolis force will build the inordinate disturbances into the orderly gradient of mean values of the corresponding elements. In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric motions.