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 con-cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynoldsexchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.Inorder to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynoldsequations is given in which the subscale motions are described by Langevin equation as the air particles are moving inthe Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchangecoefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperatureand other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be-tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancyand/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the correspondingelements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo-tions.