Rare transitions to thin-layer turbulent condensates

Abstract

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time ${\tau }_d$ of the 2-D condensate to 3-D flow state and the build-up time ${\tau }_b$ of the 2-D condensate. We show that both of these times ${\tau }_d,{\tau }_b$ follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modeled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

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• Do extreme events trigger turbulence decay? - a numerical study of turbulence decay time in pipe flows
• Mitigation of rare events in multistable systems driven by correlated noise
• Phase Transition From Turbulence To Zonal Flows In The Hasegawa-Wakatani System
• Intermittency of three-dimensional perturbations in a point-vortex model
• Spontaneous suppression of inverse energy cascade in instability-driven 2D turbulence