Condensates in thin-layer turbulence

Abstract

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly twodimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean-field three-scale model that reproduces some of the basic features of the numerical results.

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).…”

“…The two regions are separated by a critical line given by that needs to be determined. For large (weak rotation), the problem reduces to that of the non-rotating layer and therefore , where is the critical value of for the non-rotating layer (Celani et al 2010; Benavides & Alexakis 2017; van Kan& Alexakis 2019). For small , the scaling of with is not known.…”

Rare transitions to thin-layer turbulent condensates

“…In this study, we consider forced incompressible 3-D flow in a triply periodic domain of dimensions with . The set-up is identical with the one studied in van Kan & Alexakis (2019). The thin direction is referred to as the vertical ‘ ’ direction and the remaining two as the horizontal ‘ ’ directions.…”

“…2014; Favier, Guervilly & Knobloch 2019), rotating turbulence (Alexakis 2015; Yokoyama & Takaoka 2017; Seshasayanan & Alexakis 2018) and thin-layer turbulence (Xia et al. 2011; van Kan & Alexakis 2019). In many of these cases, the amplitude of the condensate state (measured by the energy in the large scales) has been shown to vary discontinuously with the system parameters.…”

“…Furthermore, close to the transition, bistability has been observed: the system was either attracted or not to the condensate state depending on the initial conditions. In particular in thin-layer flows, for values of close to , the system was attracted to either a 2-D condensate state (where most of the energy is concentrated in two counter-rotating, large-scale, 2-D vortices) or a 3-D flow state (where energy is mostly contained in 3-D small-scale fluctuations) (van Kan & Alexakis 2019; Musacchio & Boffetta 2019). The bistability in this system was accompanied by sudden ‘jumps’ between these two states.…”