Rare Event Algorithm Links Transitions in Turbulent Flows with Activated Nucleations

Bouchet, Freddy; Rolland, Joran; Simonnet, Eric

doi:10.1103/physrevlett.122.074502

Cited by 68 publications

(109 citation statements)

References 33 publications

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“…This common transition path can be seen as a low-dimensional projection of the dynamics of band splitting. Such a statistical pathway for configuration changes in a turbulent fluid system was observed in the case of barotropic jet nucleation [54].…”

Section: B Splittingmentioning

confidence: 66%

“…This characterization of the splitting pathway resembles transitions in other turbulent fluid systems for which rare-event algorithms have been applied to assess long time scales associated with infrequent events. This has been carried out in [54] for barotropic jet dynamics in the atmosphere and in [70] for a stochastic two-variable model that reproduces transitional turbulence [13]. We are currently working on applying this strategy to the study of turbulent band splitting.…”

Section: Discussionmentioning

confidence: 99%

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Statistical transition to turbulence in plane channel flow

2020

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Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette, and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code CHANNELFLOW in a narrow computational domain tilted by 24 • with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number Re cross 965, where decay and splitting lifetimes cross at greater than 10 6 advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

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Section: B Splittingmentioning

confidence: 66%

Section: Discussionmentioning

confidence: 99%

Statistical transition to turbulence in plane channel flow

2020

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“…The atmosphere itself may admit multiple equilibria. As a matter of fact, turbulent flows often exhibit coexisting steady-states for given external parameters, as well as spontaneous transitions between the two stable states, as has been reported in both numerical studies (Bouchet and Simonnet, 2009;Cortet et al, 2010;Bouchet et al, 2019) and laboratory experiments (Berhanu et al, 2007;Cortet et al, 2010;Saint-Michel et al, 2013;Michel et al, 2016). Some of these experiments (Weeks et al, 1997;Tian et al, 2001) are actually inspired by geophysical flows (Charney and DeVore, 1979).…”

Section: Introductionmentioning

confidence: 78%

Atmospheric Bistability and Abrupt Transitions to Superrotation: Wave–Jet Resonance and Hadley Cell Feedbacks

Herbert

Caballero

Bouchet

2020

Journal of the Atmospheric Sciences

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Strong eastward jets at the equator have been observed in many planetary atmospheres and simulated in numerical models of varying complexity. However, the nature of the transition from a conventional state of the general circulation, with easterlies or weak westerlies in the tropics, to such a superrotating state remains unclear. Is it abrupt or continuous? This question may have far-reaching consequences, as it may provide a mechanism for abrupt climate change in a planetary atmosphere, both through the loss of stability of the conventional circulation and through potential noise-induced transitions in the bistability range. We study two feedbacks which may lead to bistability between a conventional and a superrotating state: the Hadley cell feedback and a wave-jet resonance feedback. We delineate the regime of applicability of these two mechanisms in a simple model of zonal acceleration budget at the equator. Then, we show using numerical simulations of the axisymmetric primitive equations that the wave-jet resonance feedback indeed leads to robust bistability, while the bistability governed by the Hadley cell feedback, although observed in our numerical simulations, is much more fragile in a multilevel model.

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“…While the processes by which the flow-forming instability manifests are well understood, we lack comprehensive understanding of how this instability is equilibrated. For example, as the zonal jets grow they often merge or branch to larger or smaller scales (Danilov and Gurarie 2004;Manfroi and Young 1999), multiple turbulence-jet equilibria exist (Farrell and Ioannou 2007;Parker and Krommes 2013;Constantinou et al 2014a), and, also, transitions from various turbulent jet attractors may occur (Bouchet et al 2018). Some outstanding questions include:…”

Section: Introductionmentioning

confidence: 99%

Statistical State Dynamics of Weak Jets in Barotropic Beta-Plane Turbulence

Bakas

Constantinou

Ioannou

2019

Journal of the Atmospheric Sciences

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Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state ('zonostrophic instability') which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flowforming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the evolution of weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.

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Rare Event Algorithm Links Transitions in Turbulent Flows with Activated Nucleations

Cited by 68 publications

References 33 publications

Statistical transition to turbulence in plane channel flow

Statistical transition to turbulence in plane channel flow

Atmospheric Bistability and Abrupt Transitions to Superrotation: Wave–Jet Resonance and Hadley Cell Feedbacks

Statistical State Dynamics of Weak Jets in Barotropic Beta-Plane Turbulence

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