Inverse energy cascade in developed turbulence at the breaking of the symmetry of helical modes

Gledzer, E. B.; Chkhetiani, О. G.

doi:10.1134/s0021364015190066

Cited by 10 publications

(12 citation statements)

References 12 publications

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“…We explain this lack of helical asymmetry in the magnetic field growth by observing that the flow is nearly mirror symmetric for k > k f u , as shown in Figures 5(c-d). This is not surprising, it is well known that fully homogeneous and isotropic turbulence tends to quickly recover small-scale mirror symmetry even in presence of a large-scale helicity injection (Chen et al 2003a,b;Mininni & Pouquet 2010;Sahoo et al 2016;Gledzer & Chkhetiani 2015;Deusebio & Lindborg 2014;Kessar et al 2015;Stepanov et al 2015a,b). To quantify the rate of recovery we show in the inset of Figure 5…”

Section: R1-dmentioning

confidence: 84%

Effects of Magnetic and Kinetic Helicities on the Growth of Magnetic Fields in Laminar and Turbulent Flows by Helical Fourier Decomposition

Linkmann

Sahoo

McKay

et al. 2017

ApJ

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We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small-and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achieved for the magnetic component with the same helicity of the flow, in agreement with the Stretch-Twist-Fold mechanism. Vice versa, in presence of a Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite sign, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

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Section: R1-dmentioning

confidence: 84%

Effects of Magnetic and Kinetic Helicities on the Growth of Magnetic Fields in Laminar and Turbulent Flows by Helical Fourier Decomposition

Linkmann

Sahoo

McKay

et al. 2017

ApJ

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“…Owing to its aforementioned connection to nonlinear Navier-Stokes dynamics and its relevance to atmospheric physics (Lilly 1986), the effect of helicity has been studied in a variety of turbulent flows, including homogeneous isotropic turbulence (Chen et al 2003a,b;Kessar et al 2015;Stepanov et al 2015;Gledzer & Chkhetiani 2015;Sahoo & Biferale 2015;Alexakis 2017), rotating turbulence (Mininni & Pouquet 2010a,b) and the atmospheric boundary layer (Deusebio & Lindborg 2014). However, the dependence of β on the helicity of the external force has never been investigated analytically or numerically.…”

Section: Introductionmentioning

confidence: 99%

Effects of helicity on dissipation in homogeneous box turbulence

Linkmann

2018

J. Fluid Mech.

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The dimensionless dissipation coefficient β = εL/U 3 , where ε is the dissipation rate, U the root-mean-square velocity and L the characteristic scale of the largest flow structures, is an important characteristic of statistically stationary homogeneous turbulence. In studies of β, the external force is typically isotropic and large scale, and its helicity H f either zero or not measured. Here, we study the dependence of β on H f and find that it decreases β by up to 10% for both isotropic forces and shear flows. The numerical finding is supported by static and dynamical upper bound theory. Both show a relative reduction similar to the numerical results. That is, the qualitative and quantitative dependence of β on the helicity of the force is well captured by upper bound theory. Consequences for the value of the Kolmogorov constant and theoretical aspects of turbulence control and modelling are discussed in connection with the properties of the external force. In particular, the eddy viscosity in large eddy-simulations of homogeneous turbulence should be decreased by at least 10% in the case of strongly helical forcing.

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“…We observe that the predictions (15)- (16) give a better compensation at least for not too high wavenumbers where a dissipative bottleneck is known to affect the local scaling properties. At those wavenumbers, the relative helicity H(k)/kE(k) is already very small and it is unlikely that the bottleneck is due to some helical effects as proposed by (18). Concerning real-space quantities, in Fig.…”

Section: Numerical Simulations Of Navier-stokes Equationsmentioning

confidence: 85%

“…This lead to four independent classes of helical shell models, mimicking exactly the four classes of helical interactions of the original NSE [27]. Other models based on similar decompositions have also been proposed [18,37,38]. Here we follow the structure given in [23], where the four possible models have the general form:…”

Section: Helical Shell Modelsmentioning

confidence: 99%

“…There exist instances where helicity plays a key role, interfering with the energy transfer, as in rotating turbulence [9,10], in shear flows [11], and in the case of an NSE confined to evolve on a subset of sign-definite helical modes [12][13][14][15]. In the presence of a stationary helicity injection, we have an exact law which predicts the scaling properties of a specific velocity-vorticity mixed third-order correlation function [16][17][18]. Nevertheless, this is not a strong constraint for the whole statistics.…”

Section: Introductionmentioning

confidence: 99%

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Helicity statistics in homogeneous and isotropic turbulence and turbulence models

2017

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We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small-scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.a Version accepted for publication (postprint) on Phys. Rev. Fluids 2, 024601

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Inverse energy cascade in developed turbulence at the breaking of the symmetry of helical modes

Cited by 10 publications

References 12 publications

Effects of Magnetic and Kinetic Helicities on the Growth of Magnetic Fields in Laminar and Turbulent Flows by Helical Fourier Decomposition

Effects of Magnetic and Kinetic Helicities on the Growth of Magnetic Fields in Laminar and Turbulent Flows by Helical Fourier Decomposition

Effects of helicity on dissipation in homogeneous box turbulence

Helicity statistics in homogeneous and isotropic turbulence and turbulence models

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