Sustainment of Oscillations in Localized Turbulent Structures in Pipes

The solution of the Navier–Stokes equations which reproduces some qualitative features of localized turbulent structures developed in circular pipes at transitional Reynolds numbers is numerically investigated. In the phase space this solution corresponds to the limiting state of the solution which evolves along the separatrix dividing the regions of attraction of the solutions corresponding to the laminar and turbulent flow regimes. Relative simplicity of the spatial and temporal behavior of the limiting solution on the separatrix makes it possible to investigate it in detail. In particular, the nonlinear mechanism of the onset of streamwise vortices responsible for sustainment of near-wall streaks whose instability ensures the presence of fluctuations is revealed.