Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Sahoo, Ganapati; Pietro, Massimo De; Biferale, Luca

doi:10.1103/physrevfluids.2.024601

Cited by 13 publications

(17 citation statements)

References 41 publications

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“…More broadly, we conjecture that the phenomenon of scale-dependent phase alignment uncovered in this work may be the mechanism underpinning the joint forward cascade of two ideal invariants in other physical systems, including nonconducting fluids described by the Navier-Stokes equation [22,24,26,27].…”

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confidence: 81%

Dynamic Phase Alignment in Inertial Alfvén Turbulence

et al. 2020

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In weakly-collisional plasma environments with sufficiently low electron beta, Alfvénic turbulence transforms into inertial Alfvénic turbulence at scales below the electron skin-depth, k ⊥ de 1. We argue that, in inertial Alfvénic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale-dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as cos α k ∝ k −1 ⊥ . The kinetic and magnetic energy spectra scale as ∝ k, respectively. As a result of the dual direct cascade, the generalizedhelicity spectrum scales as ∝ k −5/3 ⊥ , implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the k ⊥ de 1 range. Turbulent eddies exhibit a phase-space anisotropy k ∝ k 5/3 ⊥ , consistent with critically-balanced inertial Alfvén fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, non-relativistic pair plasmas, as well as to strongly rotating non-ionized fluids.

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confidence: 81%

Dynamic Phase Alignment in Inertial Alfvén Turbulence

et al. 2020

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“…By forcing at large scales the dNS equations, a direct helicity cascade with E(k) ∼ ǫ 2/3 H k −7/3 was obtained. It was also notably shown that as soon as helicity is not made strictly sign-definite, by adding helical Fourier modes with the opposite helicity (negative here), the inverse energy cascade vanishes, and that the transition between the upward and forward cascades mechanisms looks singular [14,16]. On the other hand, by changing the relative weight of homochiral and heterochiral triads, one is led to a transition from direct to inverse cascade for a finite value of the control parameter [15], showing that the way Navier Stokes equations transfer energy across scales might be strongly different by changing the involved degrees of freedom.…”

Section: Introductionmentioning

confidence: 92%

“…They consequently recovered the second scenario of [3], namely an inverse cascade of kinetic energy and a forward cascade of helicity, showing that all three dimensional turbulent flows indeed possess a sub-set of Fourier interactions potentially able to sustain an inverse energy cascade. Such a "surgery" of the Navier-Stokes equations was thoroughly investigated in multiple subsequent works [14][15][16] so that the details are not recalled here. The main findings are that by forcing at small scales the decimated Navier-Stokes (dNS) equations where helicity is made sign-definite, say positive here, kinetic energy is transferred to smaller wavenumbers with E(k) ∼ ǫ 2/3 k −5/3 .…”

Section: Introductionmentioning

confidence: 99%

Closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence

2017

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We study the energy transfer properties of three dimensional homogeneous and isotropic turbulence where the non-linear transfer is altered in a way that helicity is made sign-definite, say positive. In this framework, known as homochiral turbulence, an adapted eddy-damped quasi-normal Markovian (EDQNM) closure is derived to analyze the dynamics at very large Reynolds numbers, of order 10 5 based on the Taylor scale. In agreement with previous findings, an inverse cascade of energy with a kinetic energy spectrum like ∝ k −5/3 is found for scales larger than the forcing one. Conjointly, a forward cascade of helicity towards larger wavenumbers is obtained, where the kinetic energy spectrum scales like ∝ k −7/3 . By following the evolution of the closed spectral equations for a very long time and over a huge extensions of scales, we found the developing of a non monotonic shape for the front of the inverse energy flux. The very long time evolution of the kinetic energy and integral scale in both the forced and unforced cases is analyzed also. * thomas.gomez@univ-lille1.fr 2

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“…By employing the conventional turbulence time scale ω k ∝ ε 1/3 k 2/3 , (1.2a,b) provides the conventional simultaneous or joint energy and helicity cascades range spectra (Brissaud et al 1973), (1.3a,b) where C K and C H are constants. The spectra provided by (1.3a,b) are observed in the numerical simulations of homogeneous turbulence (Borue & Orszag 1997;Chen et al 2003a,b;Mininni, Alexakis & Pouquet 2006;Baerenzung et al 2008;Sahoo, De Pietro & Biferale 2017), an observation of an atmospheric boundary layer (Koprov et al 2005), and a direct numerical simulation (DNS) of the Ekman boundary layer (Deusebio & Lindborg 2014). It should be noted that Linkmann (2018) suggested the possibility of helicity altering the value of C K , which poses a question on the universality of Kolmogorov's theory.…”

Section: Introductionmentioning

confidence: 96%

“…2003 a , b ; Mininni, Alexakis & Pouquet 2006; Baerenzung et al. 2008; Sahoo, De Pietro & Biferale 2017), an observation of an atmospheric boundary layer (Koprov et al. 2005), and a direct numerical simulation (DNS) of the Ekman boundary layer (Deusebio & Lindborg 2014).…”

Section: Introductionmentioning

confidence: 99%

Scale-similar structures of homogeneous isotropic non-mirror-symmetric turbulence based on the Lagrangian closure theory

Inagaki

2021

J. Fluid Mech.

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We investigate the effect of helicity on the scale-similar structures of homogeneous isotropic and non-mirror-symmetric turbulence based on the Lagrangian renormalised approximation (LRA), which is a self-consistent closure theory proposed by Kaneda (J. Fluid Mech., vol. 107, 1981, pp. 131–145). In this study, we focus on the time scale representing the scale-similar range. For the LRA, the Lagrangian two-time velocity correlation and response function determine the representative time scale. The LRA predicts that both the Lagrangian two-time velocity correlation and response function equation do not explicitly depend on helicity. We assume the extended scale-similar spectra and time scale by considering the helicity dissipation rate. Considering the small-scale structures, the requirements for the energy and helicity fluxes and response function equation to be scale similar, yield the conventional inertial-range power laws and provide the energy and helicity spectra $\propto k^{-5/3}$ and the time scale $\propto \varepsilon ^{-1/3} k^{-2/3}$ , where $\varepsilon$ and $k$ denote the energy dissipation rate and wavenumber, respectively. Notably, energy flux can be scale similar only when $k^H /k \ll 1$ , where $k^H = \varepsilon ^H/\varepsilon$ and $\varepsilon ^H$ denotes the helicity dissipation rate. This condition makes the energy cascade process in the scale-similar range completely independent of helicity. We also investigate the localness of the interscale interaction in the energy and helicity cascades for the LRA. We demonstrate that the helicity cascade is slightly non-local in scales compared with the energy cascade. This study provides a foundation on the modelling of non-mirror-symmetric turbulent flows.

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Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Cited by 13 publications

References 41 publications

Dynamic Phase Alignment in Inertial Alfvén Turbulence

Dynamic Phase Alignment in Inertial Alfvén Turbulence

Closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence

Scale-similar structures of homogeneous isotropic non-mirror-symmetric turbulence based on the Lagrangian closure theory

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