Bistability of the large-scale dynamics in quasi-two-dimensional turbulence

Abstract

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number $Re$ are increased, showing that the bistability is neither a finite-size nor a finite- $Re$ effect. We furthermore predict a cross-over from a bimodal regime at low box size, low $Re$ to a regime of pure hysteresis at high box size, high $Re$ , in which any transition from one state to the other is prohibited at any finite time scale.

Fluctuating landscapes and heavy tails in animal behavior

“…We have used a physics approach to shed light on biological phenomena, leveraging statistical mechanics as a framework for thinking about the effect of slowlyvarying internal states on animal behavior. Simultaneously, the observations from animal behavior also inspired new physics, leading to general results regarding the emergence of heavy tails in slowly-driven potential landscapes, a result that we believe is relevant to a wide range of natural systems in chemistry, biology, or finance (see, e.g., [44–47, 50, 105, 106] and references therein).…”

“…Notable examples include natural disasters [4] or the spreading of a virus [5]. In fact, first passage times are central to many fields within physics and beyond, with important examples stemming from chemistry, biology and finance (see, e.g., [6][7][8][9][10][11][12] and references therein). Biology in particular is ripe with examples where time is of the essence [13], such as fertilization [14], intracellular events [15][16][17][18][19][20][21], search processes (e.g., foraging or chemotaxis) [22][23][24], neural activity [25,26] or population dynamics [27].…”

Competition between Rayleigh–Bénard and horizontal convection

“…Finally, even though we have integrated these bi-stable states for up to diffusive timescales based on the height of the fluid domain, we cannot exclude the possibility that rare spontaneous transitions can occur between them (partly because the diffusive timescale based on the horizontal size of the domain scales with , hence is much longer). One way to more firmly prove that bi-stable states exist would require a detailed measurement of the transition time between different states, as was recently done in thin-layer turbulence (de Wit, van Kan & Alexakis 2022), which is beyond the scope of the present study.…”

Strong coupling of flow structure and heat transport in liquid metal thermal convection

“…The discovery of coherent structures is a hallmark of modern turbulence research. Recent studies suggest that the coherent large-scale structures in turbulence may possess different flow states characterized by different topologies (Ravelet et al 2004;de la Torre & Burguete 2007;Cortet et al 2010;Zimmerman, Triana & Lathrop 2011;Huisman et al 2014;Faranda et al 2017;de Wit, van Kan & Alexakis 2022). For example, the momentum transport in turbulent Taylor-Couette flow relies on the number of Taylor vortices (Huisman et al 2014).…”