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.