Numerical study of localized turbulent structures in a pipe

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.