Discontinuous transitions towards vortex condensates in buoyancy-driven rotating turbulence

Wit, Xander M. de; Guzmán, Andrés J. Aguirre; Clercx, Hjh Herman; Kunnen, Rudie

doi:10.1017/jfm.2022.90

Cited by 8 publications

(5 citation statements)

References 58 publications

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“…Re/(Ra Ek), is plotted versus Ra. show formation of large-scale vortices in the geostrophic turbulence regime, which is also associated with an additional increase of Re for larger Ra (Julien et al 2012a,b;de Wit et al 2022). Thus all shown scalings of /L, Nu − 1 and Re for large Ra follow the predictions (3.11)-(3.13) for the geostrophic turbulence regime.…”

Section: Resultssupporting

confidence: 59%

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Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

Song,

Shishkina,

Zhu

2024

J. Fluid Mech.

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The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times 10^{13}$ and the Ekman number down to $Ek=5\times 10^{-9}$ ) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde {Ra}\equiv Ra\, Ek^{4/3}$ as $Nu-1\propto \widetilde {Ra}^{3/2}$ , where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde {Ra}$ , the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\widetilde {Ra}$ -dependence, $Nu-1\propto \widetilde {Ra}^{3}$ .

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Section: Resultssupporting

confidence: 59%

“…2012 a , b ; de Wit et al. 2022). Thus all shown scalings of , and for large follow the predictions (3.11)–(3.13) for the geostrophic turbulence regime.…”

Section: Resultsmentioning

confidence: 99%

Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

Song,

Shishkina,

Zhu

2024

J. Fluid Mech.

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“…Favier et al (2019) performed numerical experiments taking a strong large-scale vortex as initial conditions, and showed that the formation of LSVs is subcritical and also confirmed the importance of energy transport by the non-local large-scale field. de Wit et al (2022) performed numerical experiments varying the Rayleigh number and found that there exists hysteresis and discontinuity in the transition to the LSV emergent state.…”

Section: Introductionmentioning

confidence: 99%

Large-scale vortex formation in three-dimensional rotating Rayleigh-Bénard convection

Sasaki,

Takehiro,

Yamada

2024

Fluid Dyn. Res.

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Numerical experiments are performed on three-dimensional thermal convection between parallel plates in a rotating system with a larger horizontal region than in previous studies. It is confirmed that a large-scale vortex (LSV) with positive vorticity (cyclonic) is formed over a significant part of the region and its horizontal size increases if the horizontal region is extended. The correlation analysis in the vertical direction shows that the small-scale motion has a typical structure of the baroclinic vortex of thermal convection in the rotating system, whereas the large-scale motion is a barotropic vortex that is not associated with thermal convection. A horizontal spectral analysis of the individual terms in the kinetic energy equation reveals that the nonlinear effect of the small-scale vortex motion caused by the buoyancy force induces a large-scale toroidal component, and that the LSV is maintained by the balance between the nonlinear effect and the viscous dissipation of the large-scale motion. The results of this analysis indicate the importance of kinetic energy damping mechanism for the appearance of LSVs. When weak damping operates at larger scales, it is expected that the maximum extent of the vortex appears even if the horizontal region is extended further. On the other hand, the emergence of LSVs will be prevented when strong enough damping is effective at larger scales.

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“…This work focuses on the transition towards the condensate state of such quasi-2-D systems. Remarkably, in spite of the inherently widely different nature of the considered flow systems, recent studies have revealed that all across forced rotating turbulence (Alexakis 2015;Yokoyama & Takaoka 2017;Seshasayanan & Alexakis 2018), thin-layer turbulence (van Kan & Alexakis 2019) and even the natural system of rotating convection (Favier, Guervilly & Knobloch 2019;de Wit et al 2022), the transition into the condensate is discontinuous and shows hysteresis. This gives rise to a limited bistable range in which both the quasi-2-D condensate state and the 3-D flow state can exist at the same parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Since it is now known that this bistability can also survive in natural forcing conditions (Favier et al 2019;de Wit et al 2022) and the condensate can also form, albeit at more extreme parameters, between realistic no-slip walls (Aguirre Guzmán et al 2020), we aim to investigate whether the bistable range in the condensate transition could also survive under parameter conditions that are relevant to geo-and astrophysical flows. Motivated by the remarkable similarities in the condensate transition across the different flow systems, we focus on the conceptually and computationally most basic system of forced thin-layer turbulence.…”

Section: Introductionmentioning

confidence: 99%

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

2022

Self Cite

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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.

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Discontinuous transitions towards vortex condensates in buoyancy-driven rotating turbulence

Cited by 8 publications

References 58 publications

Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

Large-scale vortex formation in three-dimensional rotating Rayleigh-Bénard convection

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

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