Kinds of local self-similarity of the velocity field of prewall turbulent flows

An analysis of dimensionalities and an approach used by Millikan [1] in analysis of mean motion are applied to investigation of the pulsational motion of three types of prewall flows of an incompressible liquid, i.e., in a boundary layer with longitudinal flow around a plate, in a round tube, and in a flat channel. It is shown that with sufficiently large Reynolds numbers there exists an interval of distances from the wall x₂, within which the integral one-point correlations and the narrow-band one-point correlations _jk do not depend on x₂. In frequency space, there exists a hyperbolic interval in which _jk=A_jku²f^-1. Here A_jk=const; u is the dynamic velocity; and f is the frequency. It is also shown that, from the point of view of the mean motion, a distinction must be made between Kármán turbulent flow with rather large Reynolds numbers and non-Kármán flow with small, but turbulent Reynolds numbers. In the latter case, the coefficients in the logarithmic profiles of the velocity and in the law of the resistance depend on the Reynolds number. The article gives an evaluation of the Reynolds number, which can be assumed to be rather large.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–42, November–December, 1976.The author considers it his pleasant duty to express his indebtedness to M. A. Kashina for furnishing experimental data.