Abstract:
The turbulent flow of a viscous incompressible fluid in a circular tube caused by a pressure drop is investigated. It is assumed that the characteristic Reynolds number, calculated from the maximum velocity of the averaged flow and the length of the pipe, is large, and the radius of the pipe is small compared to its length. To find solutions to the Navier–Stokes equations, an asymptotic method of many scales is used, in which velocities and pressures are represented as series consisting of the sum of steady and perturbed terms, instead of the traditional decomposition of the solution into time-averaged values and their fluctuations. The paper finds a viscous self-sustaining steady flow that occurs in a pipe against the background of fast turbulent fluctuations. The connection of such a solution with Prigogine's theory of dissipative structures for open nonlinear systems of parabolic type is indicated. A solution has been found for the radial steady velocity, which describes the self-induced outflow of fluid from the core of the flow to a solid/permeable wall. As a result, solutions for the longitudinal velocity have been obtained that differ markedly from the laminar regimes. A qualitative comparison with well-known experiments and works on the direct numerical simulation (DNS) has been performed.
Key words:dissipative structures, turbulent flow in a pipe, asymptotic methods, inviscid vortices.
