On a model of laminar–turbulent transition

Abstract

In the perturbation theory of a shear flow, a small-lengthscale turbulent perturbation field component developing from the pre-existing turbulence is taken into account along with the usual long-wave (smooth) component. The perturbation turbulence field is assumed to be fully developed, and to satisfy the Kolmogorov-type similarity hypotheses. At the same time the perturbations of the mean velocity field and its gradient due to turbulence are assumed to be small. Under some approximations a closed autonomous set of equations governing the evolution of the turbulent perturbation field can be obtained and qualitatively investigated. The investigation shows in particular that, depending on the initial conditions, the turbulent energy of perturbation can either increase monotonically, or decrease at first and only later start to increase.Thus, the proposed model of laminar-turbulent transition includes two mechanisms: the usual mechanism of nonlinear self-modulation of long-wave perturbation components, which prevails for small pre-existing turbulence, and the mechanism of the evolution of the small-scale pre-existing turbulence which prevails otherwise. The experimental data are discussed and confirm qualitatively the proposed model.