Abstract: Wall flows such as plane Couette flow or Hagen-Poiseuillle Pipe flow are linearly stable for all Reynolds number.As a consequence, laminar and turbulent flow can coexist in time, space and phase space: they are thus bistable. One important feature of this bistability is that the collapse of turbulence under its own fluctuations or its development under a forcing become very rare when the Reynolds number and the inverse forcing variance are increased. In this presentation, I will show how analytical and numerical rare events methods can be used to greatly accelerate the sampling of events and the study the physical processes that lead to said events. This sheds light on how the turbulent flow departs the self-sustaining process of turbulence to laminarise. Streamwise long laminar holes are formed inside turbulence and extend in the spanwise direction. Locally, this laminarisation happens through the failure of streamwise vortices followed by the decay of velocity streaks.This mechanism may influence the way the lifetime of turbulence depends on the Reynolds number and the streamwise and spanwise sizes of the flow.
References:
- J. Rolland, Extremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows. Physical Review E 97.2 (2018): 023109.
- J. Rolland, Collapse of transitional wall turbulence captured using a rare events algorithm. arXiv preprint arXiv:2103.16460 (2021).
Figure: Spatio temporal diagram of contours of one minus the velocity during the collapse of turbulence, in a model of pipe flow (See J. Rolland Phys. Rev. E (2018) for details)