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 noise and long-term memory of coherent structures in a turbulent shear flow

Pereira, Michaël; Gissinger, Christophe; Fauve, S.

doi:10.1103/physreve.99.023106

Cited by 18 publications

(15 citation statements)

References 30 publications

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“…At low k c (or high Rh for Navier-Stokes), zonal mean flow reversals become less and less probable and eventually are no longer observed in the duration of the simulation. These two scenarios of emergence and disappearance of reversals have also been observed in other contexts [25,33,39,40] and hence we believe that they are generic.…”

Section: Minimal Model: Truncated Euler Equationsupporting

confidence: 81%

Transitions between turbulent states in a two-dimensional shear flow

Dallas¹,

Seshasayanan²,

Fauve³

2019

Preprint

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We study the bifurcations of the large scale zonal jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The bifurcations are seen in the probability density function (PDF) of the largest scale mode with the control parameter being the Reynolds number based on the friction coefficient denoted as Rh. As one increases Rh in the turbulent regime, the PDF of the large scale mode first bifurcates from a Gaussian to a bimodal behaviour, signifying the emergence of reversals of the zonal mean flow where the flow fluctuates between two distinct turbulent states. Futher increase in Rh leads to a bifurcation from bimodal to unimodal PDF which denotes the disappearance of the reversals of the largest scale mode. We attribute the latter transition to the long-time memory that the large scale flow exhibits related to low frequency 1/f α type of noise with 0 < α < 2. We also demonstrate that a minimal model with 15 modes, obtained from the truncated Euler equation, is able to capture the bifurcations of the large scale zonal jets exhibited by the Navier-Stokes equations.

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Section: Minimal Model: Truncated Euler Equationsupporting

confidence: 81%

Transitions between turbulent states in a two-dimensional shear flow

Dallas¹,

Seshasayanan²,

Fauve³

2019

Preprint

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“…The study of the frequency spectrum of turbulent convec-tion has been primarily directed towards the inertial range in order to make comparisons between the classical theories (Kolmogorov 1941;Bolgiano 1959;Obukhov 1959), which are based on the spatial spectrum, and experiments (Sano et al 1989;Ashkenazi & Steinberg 1999;Wu et al 1990;Shang & Xia 2001;Liot et al 2016), where the data is primarily temporal in nature, with the objective of understanding the nature of the turbulence. The low frequency portion of the spectrum has received far less attention, with the majority of prior interest coming from the classical area of "1/ noise" (Dmitruk & Matthaeus 2007;Pereira et al 2019;. Our results suggest that an understanding of the frequency spectrum of convection may allow us to predict the effective viscosity acting on the equilibrium tide for low and intermediate frequencies (though perhaps not for high frequencies).…”

Section: Discussionmentioning

confidence: 80%

Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

Duguid

Barker

Jones

2020

Monthly Notices of the Royal Astronomical Society

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Turbulent convection is thought to act as an effective viscosity (νE) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency (ω) exceeds the turnover frequency of the dominant convective eddies (ωc). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, and here we explore a wider range of parameters. We obtain several new results: 1) νE is frequency-dependent, scaling as ω−0.5 when ω/ωc ≲ 1, and appears to attain its maximum constant value only for very small frequencies (ω/ωc ≲ 10−2). This frequency-reduction for low frequency tidal forcing has never been observed previously. 2) The frequency-dependence of νE appears to follow the same scaling as the frequency spectrum of the energy (or Reynolds stress) for low and intermediate frequencies. 3) For high frequencies (ω/ωc ≳ 1 − 5), νE∝ω−2. 4) The energetically-dominant convective modes always appear to contribute the most to νE, rather than the resonant eddies in a Kolmogorov cascade. These results have important implications for tidal dissipation in convection zones of stars and planets, and indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited. We briefly touch upon the implications for planetary orbital decay around evolving stars.

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“…However, this is more probably an occurrence of 1/ω α turbulent noise (Niemann et al 2013), which is a robust feature of various turbulent flows (e.g. Herault et al 2015a;Pereira et al 2019). This power spectrum may thus exist in turbulent stellar (or planetary) interiors, resulting from the long-term properties of the turbulent flows (according to prior statistical theories, e.g.…”

Section: Astrophysical Implicationsmentioning

confidence: 97%

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Vidal

Barker

2020

Monthly Notices of the Royal Astronomical Society

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Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency |ωt| exceeds the turnover frequency ωcv of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity νE acting on the tidal flow when |ωt|/ωcv ≳ 1. We demonstrate that the frequency reduction of νE is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade (|ωt|/ωcv ∼ 1 − 5), the frequency spectrum displays an anomalous 1/ωα power law that is responsible for the frequency-reduction νE∝1/|ωt|α, where α < 1 depends on the model parameters. We then get |νE|∝1/|ωt|δ with δ > 1 for higher frequencies, and δ = 2 is obtained for a Kolmogorov turbulent cascade. A generic |νE|∝1/|ωt|2 suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

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1/f noise and long-term memory of coherent structures in a turbulent shear flow

Cited by 18 publications

References 30 publications

Transitions between turbulent states in a two-dimensional shear flow

Transitions between turbulent states in a two-dimensional shear flow

Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

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