A representation of interaction in turbulence theory

Kolmogorov's (1941) phenomenological theory of the local structure of turbulence is based on the hypothesis that energy transfer occurs among pulsations of similar scale. In the Euler description of turbulence, the transfer effect leads to a pronounced statistical dependence of pulsations of different scale. The representation of interaction proposed in the present paper is intermediate between the Lagrange and Euler representations of turbulence. Transport of small-scale by large-scale pulsations does not occur in this representation. For the statistical characteristics of the velocity field, there arises the universal problem of strong interaction. The moments and response function of Euler velocity can be obtained by averaging with respect to transports of large-scale pulsations in turbulent flow.