Do extreme events trigger turbulence decay? - a numerical study of turbulence decay time in pipe flows

Abstract

Turbulence locally created in laminar pipe flows shows sudden decay or splitting after a stochastic waiting time. In laboratory experiments, the mean waiting time was observed to increase double-exponentially as the Reynolds number (Re) approaches its critical value. To understand the origin of this double-exponential increase, we perform many pipe flow direct numerical simulations of the Navier-Stokes equations, and measure the cumulative histogram of the maximum axial vorticity field over the pipe (turbulence intensity). In the domain where the turbulence intensity is not small, we observe that the histogram is well-approximated by the Gumbel extreme-value distribution. The smallest turbulence intensity in this domain roughly corresponds to the transition value between the locally stable turbulence and a meta-stable (edge) state. Studying the Re dependence of the fitting parameters in this distribution, we derive that the time scale of the transition between these two states increases double-exponentially as Re approaches its critical value. On the contrary, in smaller turbulence intensities below this domain, we observe that the distribution is not sensible to the change of Re. This means that the decay time of the meta-stable state (to the laminar state) is stochastic but Re-independent in average. Our observation suggests that the conjecture made by Goldenfeld et al. to derive the double-exponential increase of turbulence decay time is approximately satisfied in the range of Re we studied. We also discuss using another extreme-value distribution, Fréchet distribution, instead of the Gumbel distribution to approximate the histogram of the turbulence intensify, which reveals interesting perspectives.

arXiv comment18 pages, 10 figures

References in corpus (20)

• Sampling rare switching events in biochemical networks
• Cascades and transitions in turbulent flows
• Direct evaluation of large-deviation functions
• Simplifying the complexity of pipe flow
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Population dynamics method with a multi-canonical feedback control
• On the transient nature of localized pipe flow turbulence
• The instanton method and its numerical implementation in fluid mechanics
• The Openpipeflow Navier--Stokes Solver
• A rare event algorithm links transitions in turbulent flows with activated nucleations
• Large negative velocity gradients in Burgers turbulence
• Critical Transitions in Thin Layer Turbulence
• Turbulence as a problem in non-equilibrium statistical mechanics
• Extreme fluctuations and the finite lifetime of the turbulent state
• Computing return times or return periods with rare event algorithms
• Split energy cascade in turbulent thin fluid layers
• Relevance of instantons in Burgers turbulence
• Rare transitions to thin-layer turbulent condensates
• Instantons in a Lagrangian model of turbulence
• Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

Cited by in corpus (5)

• Extreme events in transitional turbulence
• Routes to turbulence in Taylor-Couette flow
• Bistability of the large-scale dynamics in quasi-two-dimensional turbulence
• Lifetimes of metastable windy states in two-dimensional Rayleigh-Bénard convection with stress-free boundaries
• Extreme-value statistics of curl-of-vorticity precursor peaks in perturbed Taylor-Green vortex turbulence