Working Paper Article Version 1 This version is not peer-reviewed

Transitional Channel Flow: A Minimal Stochastic Model

Version 1 : Received: 2 November 2020 / Approved: 4 November 2020 / Online: 4 November 2020 (09:16:57 CET)

A peer-reviewed article of this Preprint also exists.

Manneville, P.; Shimizu, M. Transitional Channel Flow: A Minimal Stochastic Model. Entropy 2020, 22, 1348. Manneville, P.; Shimizu, M. Transitional Channel Flow: A Minimal Stochastic Model. Entropy 2020, 22, 1348.


In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton evolving von Neumann neighbourhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.


transition to/from turbulence; wall-bounded shear flow; plane Poiseuille flow; spatiotemporal intermittency; directed percolation; critical phenomena


Physical Sciences, Acoustics

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