Statistical description of a chain of interacting Taylor vortices in the direct interaction approximation

It is shown that the traditional method of statistical description of a developed hydrodynamic turbulence (using Wyld's diagram technique, 1961), may also be suitable for describing turbulence generation, for the case when the number of effectively excited degrees of freedom is small (less than 5) for intermediate Reynolds numbers, and when the motion of the liquid is already randomized. The second moments of the distribution function for noncoinciding times, describing the statistics of azimuthal (flexural) modes, are calculated for a chain of interacting Taylor vortices, arising as a result of the loss of stability of the Couette flow, with a rotating internal cylinder. The direct interaction approximation, which does not take vortex renormalization into consideration, is used and good qualitative agreement is found with the results of the numerical experiment of L'vov et al. (1981).