Laminar-Turbulent Patterning in Transitional Flows

Abstract

Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an upper threshold Rt above which turbulence is uniform (featureless) and a lower threshold Rg below which any form of turbulence decays, possibly at the end of overlong chaotic transients. The most emblematic cases of flow along flat plates transiting to/from turbulence according to this scenario are reviewed. The coexistence is generally in the form of bands, alternatively laminar and turbulent, and oriented obliquely with respect to the general flow direction. The final decay of the bands at Rg points to the relevance of directed percolation and criticality in the sense of statistical-physics phase transitions. The nature of the transition at Rt where bands form is still somewhat mysterious and does not easily fit the scheme holding for pattern-forming instabilities at increasing control parameter on a laminar background. In contrast, the bands arise at Rt out of a uniform turbulent background at a decreasing control parameter. Ingredients of a possible theory of laminar-turbulent patterning are discussed.

29 pages, 5 illustrations, written for special issue on "Complex Systems, Non-Equilibrium Dynamics and Self-Organisation" of journal Entropy edited by Dr. G. Pruessner

References in corpus (26)

• High Reynolds number Taylor-Couette turbulence
• The Significance of Simple Invariant Solutions in Turbulent Flows
• Universal scaling behavior of non-equilibrium phase transitions
• Visualizing the geometry of state space in plane Couette flow
• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• The rise of fully turbulent flow
• A Universal Transition to Turbulence in Channel Flow
• Mean flow of turbulent-laminar patterns in plane Couette flow
• Simplifying the complexity of pipe flow
• Scale invariance at the onset of turbulence in Couette flow
• Universal continuous transition to turbulence in a planar shear flow
• Turbulent-laminar patterns in plane Poiseuille flow
• Transient Turbulence in Taylor-Couette Flow
• From temporal to spatiotemporal dynamics in transitional plane Couette flow
• On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
• Transition to turbulence in wall-bounded flows: Where do we stand?
• Modeling transitional plane Couette flow
• Turbulent-laminar patterns in shear flows without walls
• On modelling transitional turbulent flows using under-resolved direct numerical simulations: The case of plane Couette flow
• Large scale flow around turbulent spots
• Turbulent bifurcations in intermittent shear flows: from puffs to oblique stripes
• Turbulent patterns in wall-bounded flows: a Turing instability?
• On the growth of laminar-turbulent patterns in plane Couette flow
• Growth dynamics of turbulent spots in plane Couette flow
• An experimental study on turbulent-stripe structure in transitional channel flow
• Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model

Cited by in corpus (6)

• Extended localized structures and the onset of turbulence in channel flow
• Transition to turbulence in shear flows
• Patterns in transitional shear turbulence. Part 2: Emergence and optimal wavelength
• Transitional channel flow: A minimal stochastic model
• Model for transitional turbulence in a planar shear flow
• Discontinuous transition to shear flow turbulence