Quasi-two-dimensional turbulence

Alexakis, Alexandros

doi:10.1007/s41614-023-00134-3

Cited by 2 publications

(2 citation statements)

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“…There is also extensive literature on experimental studies of quasi-2-D large-scale condensation (Sommeria 1986;Paret & Tabeling 1997;Xia et al 2011;Xia & Francois 2017;Fang & Ouellette 2021). Recent reviews of quasi-2-D turbulence are provided by Alexakis & Biferale (2018) and Alexakis (2023).…”

Section: Introductionmentioning

confidence: 99%

“…Eddy viscosity, including that with a negative sign, has been studied in a variety of 2-D and 3-D flows (Kraichnan 1976;Sivashinsky & Yakhot 1985;Bayly & Yakhot 1986;Yakhot & Sivashinsky 1987;Dubrulle & Frisch 1991;Gama, Vergassola & Frisch 1994;Alexakis 2018). Negative eddy viscosities are also encountered in applications within the context of backscatter parametrisations (Prugger, Rademacher & Yang 2022, 2023. Schemes of this type are used in ocean modelling (Jansen & Held 2014;Juricke et al 2020).…”

Section: Introductionmentioning

confidence: 99%

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From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence

van Kan,

Favier,

Julien

et al. 2024

J. Fluid Mech.

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We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusivity of individual vortices using ideas from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of non-trivial SV states in this system, specifically the emergence and melting of a vortex crystal.

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