Bifurcations to turbulence in transitional channel flow

Abstract

In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatio-temporal fluctuating patterns of localized turbulence along its way from/to featureless turbulence. By direct numerical simulation, we study the observed inconsistency between turbulence decay according to a two-dimensional directed-percolation (2D-DP) scenario and the presence of sustained oblique localized turbulent bands (LTBs) below the DP critical point. Above Reynolds number Reg \sim 700 sustained LTBs are observed; most LTBs have the same orientation so that the spanwise symmetry of the LTB pattern is broken below Re2 \sim 1000. The frequency of transversal splitting, by which an LTB generates another one with opposite obliqueness, so that turbulence spreading becomes intrinsically two dimensional, increases in the range Reg < Re < Re2. It reaches a critical rate at Re2 beyond which symmetry is restored. 2D-DP behavior is retrieved only above Re2. A mean-field model is proposed which qualitatively accounts for the above symmetry-restoring bifurcation by considering interactions between space-averaged densities of LTBs propagating in either direction.

v2: 36 pages, 12 figures and 9 videos. Resolutions of figures and videos are reduced

References in corpus (6)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Universal continuous transition to turbulence in a planar shear flow
• Turbulent-laminar patterns in plane Poiseuille flow
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• Extended localized structures and the onset of turbulence in channel flow
• Turbulent bifurcations in intermittent shear flows: from puffs to oblique stripes

Cited by in corpus (24)

• Statistical transition to turbulence in plane channel flow
• The phase transition to turbulence in spatially extended shear flows
• The growth mechanism of turbulent bands in channel flow at low Reynolds numbers
• Extreme events in transitional turbulence
• Structured input-output analysis of transitional wall-bounded flows
• Flow Statistics in the Transitional Regime of Plane Channel Flow
• Linear instability of turbulent channel flow
• Trigger turbulent bands directly at low Reynolds numbers in channel flow using a moving-force technique
• Direct path from turbulence to time-periodic solutions
• Decay of streaks and rolls in plane Couette-Poiseuille flow
• Patterns in transitional shear turbulence. Part 2: Emergence and optimal wavelength
• Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction
• Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows
• Propagation mechanism of localized wave packet in plane-Poiseuille flow
• Linear and nonlinear optimal growth mechanisms for generating turbulent bands
• Transitional channel flow: A minimal stochastic model
• Linear stability of turbulent channel flow with one-point closure
• A traveling wave bifurcation analysis of turbulent pipe flow
• Pattern preservation during the decay and growth of localized wave packet in two-dimensional channel flow
• Size-dependent transient nature of localized turbulence in transitional channel flow
• Aging and memory of transitional turbulence
• Model for transitional turbulence in a planar shear flow
• Large-scale streak instabilities of transitional channel flow
• Stability of plane Couette and Poiseuille flows rotating about the streamwise axis