THE DIFFUSION IN MULTI-SCALING ATMOSPHERIC TURBULENCE

In this paper the high order ordinary differential equation of auto-correlation function is obtained on the basis of the Langevian equation group that comes from the Monte Carlo relations between each order fluctuation and the next order in the steady, homogeneous atmospheric turbulence multiscaled with various averaging time. The general solution of the auto-correlation equation is a sum of series exponential functions with different time scale and coefficients that indicate the ratio of each scaling turbulence energy to the total energy of the turbulence. The eddy diffusion parameter accordingly can be divided into several parts that present the contributions made by different time scale autocorrelation in the Taylor's integration. For e!cample the Pasquill-Gifford experimental diffusion parameter (D) could be represented as a sum of three terms respectively with time scale 4,35 and 240 seconds when travel time is up to 400 second. The longer the plume travel tune, the longer the time scale occur in the sum. The analysis in this paper also points out that the large time scale eddies contribute much more to the eddy transfer coefficients than small one in the long travel time. According to the multi-scaling concept the diffusion parameters can be easily represented as a function of atmospheric turbulence parameters which have more physical significance.