THE RELATION BETWEEN MARKOV PROCESS THEORY AND KOLMOGOROFF’S THEORY OF TURBULENCE AND THE EXTENSION OF KOLMOGOROFF’S LAWS I.An Analysis of the Relation between the two Theories

The whole paper consists of two parts(Part Ⅰ and Part Ⅱ).In part Ⅰ,we shall analyze the relation between the two theories of turbulenceinvolving large Reynolds number:the Markov process theory from the La-grangian point of view and Kolmogoroff’s theory from the Eulerian pointof view.It will be pointed out that the Reynolds number needed forthe markovian description of turbulence should be as large as that neededfor Kolmogoroff’s second hypothesis,that the eddies of the period oforder T.(the self-correlation time scale of the random velocity u)andthe eddies of the period of order T(the self-correlation time scaleof the random force f)correspond to the energy-containing eddies andthe eddies in the dissipation range respectively,and that T≤t≤β,the time interval for the applicability of Richardson’s law during two-particle’s dispersion,corresponds to the inertial subrange in Kolmo-goroff’s theory.Thus,these two theories reflect the property of theturbulence involving very large Reynold