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Kinematics and Dynamics of Turbulent Bands at Low Reynolds Numbers in Channel Flow
Article

Transitional Channel Flow: A Minimal Stochastic Model

1
LadHyX, École Polytechnique, CNRS, Institut Polytechnique de Paris, 91128 Palaiseau, France
2
Graduate School of Engineering Science, Osaka University, Toyonaka 560-0043, Japan
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(12), 1348; https://doi.org/10.3390/e22121348
Received: 2 November 2020 / Revised: 24 November 2020 / Accepted: 24 November 2020 / Published: 29 November 2020
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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 of evolving von Neumann neighborhoods 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 an 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. View Full-Text
Keywords: transition to/from turbulence; wall-bounded shear flow; plane Poiseuille flow; spatiotemporal intermittency; directed percolation; critical phenomena transition to/from turbulence; wall-bounded shear flow; plane Poiseuille flow; spatiotemporal intermittency; directed percolation; critical phenomena
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MDPI and ACS Style

Manneville, P.; Shimizu, M. Transitional Channel Flow: A Minimal Stochastic Model. Entropy 2020, 22, 1348. https://doi.org/10.3390/e22121348

AMA Style

Manneville P, Shimizu M. Transitional Channel Flow: A Minimal Stochastic Model. Entropy. 2020; 22(12):1348. https://doi.org/10.3390/e22121348

Chicago/Turabian Style

Manneville, Paul; Shimizu, Masaki. 2020. "Transitional Channel Flow: A Minimal Stochastic Model" Entropy 22, no. 12: 1348. https://doi.org/10.3390/e22121348

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