Statistical transition to turbulence in plane channel flow

Abstract

Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by $24^{\circ }$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number $R{e}_{\text{cross}}\simeq 965$, where decay and splitting lifetimes cross at greater than $10^6$ advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

arXiv comment17 pages, 16 figures

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Cited by in corpus (16)

• The phase transition to turbulence in spatially extended shear flows
• Extreme events in transitional turbulence
• Flow Statistics in the Transitional Regime of Plane Channel Flow
• Rare event-triggered transitions in aerodynamic bifurcation
• Collapse of transitional wall turbulence captured using a rare events algorithm
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• Phase transition to turbulence via moving fronts
• Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows
• Linear and nonlinear optimal growth mechanisms for generating turbulent bands
• Transitional channel flow: A minimal stochastic model
• Lifetimes of metastable windy states in two-dimensional Rayleigh-Bénard convection with stress-free boundaries
• Far field of turbulent spots
• 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