Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Abstract

Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-to-laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number R_{low}, whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond R_{low}.

9 pages, 3 figures, published in 2009 as a Rapid Communication in Phys. Rev. E, vol. 79, article 025301, corrected to include erratum Phys. Rev. E 79, 039904. References to now published material have been updated. A note has been added pointing to recent related work by D. Barkley (arXiv:1101.4125v1)

References in corpus (6)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'
• Highly-symmetric travelling waves in pipe flow
• Modeling transitional plane Couette flow
• Large scale flow around turbulent spots
• Understanding the sub-critical transition to turbulence in wall flows

Cited by in corpus (4)

• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
• Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model
• Formation of spanwise vorticy in oblique turbulent bands of transitional plane Couette flow, part 1: Numerical experiments