On the Mechanism of Turbulent Shear Flows
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
On the Mechanism of Turbulent Shear Flows V. P. Vorotilin* Institute of Applied Mechanics, Russian Academy of Sciences, Leningradskii pr. 7, Moscow, 125040 Russia *e-mail: [email protected] Received January 14, 2019; revised January 14, 2019; accepted February 1, 2019
Abstract—As a result of our analysis of some facts of turbulent flows, whose explanation is beyond the scope of existing semiempirical theories, in particular, our estimate of the effective roughness height in pipes with distributed roughness characterized by two or more length scales, we present a version of the theory of turbulent flows in channels with smooth and rough walls with a unified mechanism of the dynamic interaction (friction mechanism) of a turbulent flow with its boundaries—the channel walls or external laminar flow. We have derived the expressions for a generalized law of friction that describe a turbulent flow at all admissible Reynolds numbers from the regime of flow with smooth walls to the regime with a complete manifestation of roughness elements and for sand roughness consistent with Nikuradse’s experimental data. One of the conclusions of the theory is the assertion that the only source of turbulence for turbulent flows in channels and jets are the vortices forming near the walls of channels and at the free boundaries of turbulent jets, and only through these vortices is the kinetic energy from the mean flow converted to the energy of turbulent pulsations. The difference between the mechanisms of the laminar and turbulent flow regimes can be clearly represented by Eq. (24). DOI: 10.1134/S1063776119060165
1. INTRODUCTION Despite the inexhaustible flow of publications devoted to theoretical and applied problems of turbulent flows over decades [1–10], there remain many, as noted in the review paper [1], challenging questions concerning both a general understanding of the turbulence mechanism and specific calculations, in particular, the calculations of turbulent flows in channels with rough walls [11–15]. According to the prevalent views of turbulence, calculating the velocity field has almost always remained the main goal of the theoretical models designed to solve specific problems of turbulent flows [16, 17], because the velocity as a soughtfor variable enters into the averaged Navier–Stokes equations, which are the basic equations for the subsequent development of model methods to describe turbulent flows. The above considerations are usually tacitly taken as self-evident truths and, in this case, are mentioned in connection with the attempts at an alternative approach to solving the problems of turbulent flows under consideration. The motive for the statement of this problem was the conclusion from [18] that the only source of turbulence for turbulent jets are the vortices forming as a result of the turbulent friction of an external flow at the jet boundary, and only through these vortices is the kinetic energy from the mean flow converted to the energy of turbulent pulsations. Th
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