Abstract
A viscous incompressible flow in a circular pipe is studied numerically at the transitional Reynolds number Re = 2200. The limiting solution of the Navier–Stokes equations is investigated, which arises on a separatrix between the attraction regions of the solutions corresponding to laminar and turbulent flow regimes in the phase space. The solution has the form of a structure, localized in space and traveling downstream, which in some qualitative characteristics is similar to the turbulent puffs observed experimentally in the range of transitional Reynolds numbers. A typical property of the limiting solution on the separatrix is its conditional time periodicity (in the moving reference frame), which makes it possible to investigate in detail the self-sustainment mechanism of this solution. In the moving reference frame, the limiting solution can be represented as the superposition of the averaged steady-state flow and periodic fluctuations. It is shown that the fluctuations develop due to the linear instability of the mean flow, different from the Kelvin–Helmholtz instability.
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Original Russian Text © N.V. Nikitin, V.O. Pimanov, 2015, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2015, Vol. 50, No. 5, pp. 64–75.
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Nikitin, N.V., Pimanov, V.O. Numerical study of localized turbulent structures in a pipe. Fluid Dyn 50, 655–664 (2015). https://doi.org/10.1134/S0015462815050075
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DOI: https://doi.org/10.1134/S0015462815050075