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 τ d of the 2-D condensate to 3-D flow state and the build-up time τ b of the 2-D condensate. We show that both of these times τ d , τ 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.

Critical transition in fast-rotating turbulence within highly elongated domains

“…Similar transitions from a forward to an inverse cascade and to quasi-2-D motion have also been observed in other systems like thin-layer turbulence (Celani, Musacchio & Vincenzi 2010; Benavides & Alexakis 2017; Musacchio & Boffetta 2017; van Kan & Alexakis 2019; van Kan, Nemoto & Alexakis 2019; Musacchio & Boffetta 2019), stratified turbulence (Sozza et al 2015), rotating and stratified flows (Marino, Pouquet & Rosenberg 2015), magneto-hydrodynamic systems (Alexakis 2011; Seshasayanan, Benavides & Alexakis 2014; Seshasayanan & Alexakis 2016) and helically constrained flows (Sahoo & Biferale 2015; Sahoo, Alexakis & Biferale 2017) among others (see the articles by Alexakis & Biferale (2018) and Pouquet et al (2019) for recent reviews).…”

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

“…It would be interesting to ask if the Fréchet distribution fits better in their case as well with more detailed statistics. Furthermore, turbulent transitions between two- and three-dimensional dynamics have been long studied (Smith, Chasnov & Waleffe 1996; Celani, Musacchio & Vincenzi 2010; Benavides & Alexakis 2017; Musacchio & Boffetta 2017; Alexakis & Biferale 2018), where a super-exponential increase of the transition time was observed in thin-layer turbulent condensates (van Kan, Nemoto & Alexakis 2019). This super-exponential increase could be also studied using the extreme value theory.…”

Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence

“…This was obtained, for fluid dynamics, for example through a Fourier analysis of ocean drifters [54,55], as well as in laboratory and numerical experiments of strongly rotating flows in the presence or not of stratification [56][57][58][59]. It is also observed in three-dimensional fluid dynamics in thin layers, with a clear threshold behavior [60,61]. In MHD, similar detailed analyses were performed on numerical data in two and three space dimensions [62,63], as well as in the solar wind [19], and more recently in the atmosphere of Jupiter [64].…”