Conformal Invariance in Three-Dimensional Rotating Turbulence

Thalabard, Simon; Rosenberg, Duane; Pouquet, A.; Mininni, Pablo D.

doi:10.1103/physrevlett.106.204503

Cited by 12 publications

(15 citation statements)

References 17 publications

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“…The values of the cancellation exponent found in this study confirm a phenomenological relation for conformal invariant systems between the cancellation exponent and the diffusivity of the Brownian process in the equivalent SLE system derived in Ref. [41].…”

Section: Discussionsupporting

confidence: 70%

“…For the particular case of rotating helical turbulence, in Ref. [41] it was found that only the vertically averaged vertical velocity and vorticity display conformally invariant behavior, with the same scaling for both the vertical velocity and vertical vorticity, and with κ SLE = 3.6 ± 0.1 measured for the vertical vorticity. It is important to note that the relation given by Eq.…”

Section: Cancellation Exponentmentioning

confidence: 99%

“…For conformally invariant properties of the flow, another phenomenological relation between the cancellation exponent and Brownian diffusivity in conformally invariant processes belonging to a class of Schramm-Löwner evolution (SLE) was obtained in Ref. [41],…”

Section: Cancellation Exponentmentioning

confidence: 99%

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Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

Horne

Mininni

2013

Phys. Rev. E

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We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically averaged fields. Data for the analysis are provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536 3 grid points, with Reynolds numbers between ≈1100 and ≈5100, and with moderate Rossby numbers between ≈0.06 and ≈8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation, only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of an infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.

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Section: Discussionsupporting

confidence: 70%

Section: Cancellation Exponentmentioning

confidence: 99%

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Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

Horne

Mininni

2013

Phys. Rev. E

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“…Moreover, the two-dimensional inverse cascade for fluids has been found to be conformal invariant [32], making the bridge between turbulence and critical phenomena more evident. Conformal invariance has also been detected in three dimensions in the presence of strong rotation [33].…”

mentioning

confidence: 92%

Dual constant-flux energy cascades to both large scales and small scales

et al. 2017

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In this paper, we present an overview of concepts and data concerning inverse cascades of excitation towards scales larger than the forcing scale in a variety of contexts, from two-dimensional fluids and wave turbulence, to geophysical flows in the presence of rotation and stratification. We briefly discuss the role of anisotropy in the occurrence and properties of such cascades. We then show that the cascade of some invariant, for example the total energy, may be transferred through nonlinear interactions to both the small scales and the large scales, with in each case a constant flux. This is in contrast to the classical picture, and we illustrate such a dual cascade in the context of atmospheric and oceanic observations, direct numerical simulations and modeling.We also show that this dual cascade of total energy can in fact be decomposed in some cases into separate cascades of the kinetic and potential energies, provided the Froude and Rossby numbers are small enough. In all cases, the potential energy flux remains small, of the order of 10% or less relative to the kinetic energy flux. Finally, we demonstrate that, in the small-scale inertial range, approximate equipartition between potential and kinetic modes is obtained, leading to an energy ratio close to one, with strong departure at large scales due to the dominant kinetic energy inverse cascade and piling-up at the lowest spatial frequency, and at small scales due to unbalanced dissipation processes, even though the Prandtl number is equal to one.

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“…As the diffusivity of the Brownian driving function varies, a continuum of universality classes is obtained, and correspondences to numerous models in statistical mechanics have been discovered, including the Ising model [6] (even in three dimensions [7]), spin glasses [8], the Ashkin-Teller model [9], the Potts model [10], walks and polymers on the lattice [1,11,12,13], non-equilibrium phenomena [14,15] (even in three dimensions [16]), and the Gaussian free field [17]. A deep connection to Conformal Field Theory (CFT) has been unveiled [18], as well as with logarithmic CFT [19,20], and some generalizations of SLE have been based on it [21,22,23,24].…”

Section: Introductionmentioning

confidence: 99%

q-Deformed Loewner Evolution

Nigro

2013

J Stat Phys

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The Loewner equation, in its stochastic incarnation introduced by Schramm, is an insightful method for the description of critical random curves and interfaces in twodimensional statistical mechanics. Two features are crucial, namely conformal invariance and a conformal version of the Markov property. Extensions of the equation have been explored in various directions, in order to expand the reach of such a powerful method. We propose a new generalization based on q-calculus, a concept rooted in quantum geometry and non-extensive thermodynamics; the main motivation is the explicit breaking of the Markov property, while retaining scale invariance in the stochastic version. We focus on the deterministic equation and give some exact solutions; the formalism naturally gives rise to multiple mutually-intersecting curves. A general method of simulation is constructed -which can be easily extended to other q-deformed equations -and is applied to both the deterministic and the stochastic realms. The way the q = 1 picture converges to the classical one is explored as well.

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Conformal Invariance in Three-Dimensional Rotating Turbulence

Cited by 12 publications

References 17 publications

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

Dual constant-flux energy cascades to both large scales and small scales

q-Deformed Loewner Evolution

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