Role of helicity for large- and small-scale turbulent fluctuations

Sahoo, Ganapati; Bonaccorso, Fabio; Biferale, Luca

doi:10.1103/physreve.92.051002

Cited by 30 publications

(46 citation statements)

References 41 publications

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“…This is attributed to the fact that the second quadratic invariant, Helicity, becomes sign-definite for such subset of interactions. It was also observed [20] that presence of few percent of modes with opposite sign of helicity at all scales changes the direction of energy transfer in a singular manner; even though triads of classes II, III and IV are a small fraction of Class-I, they efficiently transfer energy to the small scales. It would therefore be important to study a system without the triads of Class-I in order to highlight their role in the dynamics of full Navier-Stokes equations.…”

Section: Helically Decomposed Navier-stokes Equationsmentioning

confidence: 98%

Energy cascade and intermittency in helically decomposed Navier–Stokes equations

Sahoo¹,

Biferale²

2018

Fluid Dyn. Res.

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We study the nature of the triadic interactions in Fourier space for threedimensional Navier-Stokes equations based on the helicity content of the participating modes. Using the tool of helical Fourier decomposition we are able to access the effects of a group of triads on the energy cascade process and on the small-scale intermittency. We show that while triadic interactions involving modes with only one sign of helicity results to an inverse cascade of energy and to a complete depletion of the intermittency, absence of such triadic interactions has no visible effect on the energy cascade and on the inertial-range intermittency of the three-dimensional Navier-Stokes equations.

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Section: Helically Decomposed Navier-stokes Equationsmentioning

confidence: 98%

Energy cascade and intermittency in helically decomposed Navier–Stokes equations

Sahoo¹,

Biferale²

2018

Fluid Dyn. Res.

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“…Their normalized fourth orders are chosen to illustrate their statistical discrepancy, which is related to the intermittency representing the strong non-Gaussian fluctuations. It could be assessed quantitatively by excess kurtosis [14,31]. In Fig.4, we exhibit the excess kurtosis of the first-and second-channel helicity flux and energy flux, respectively.…”

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confidence: 99%

Dual channels of helicity cascade in turbulent flows

Yan

et al. 2020

J. Fluid Mech.

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Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulence. From the traditional viewpoint, there exists only one channel of helicity cascade similar to that of kinetic energy cascade. Through theoretical analysis, we find that there are two channels in helicity cascade process. The first channel mainly originates from vortex twisting process, and the second channel mainly originates from vortex stretching process. By analysing the data of direct numerical simulations of typical turbulent flows, we find that these two channels behave differently. The ensemble averages of helicity flux in different channels are equal in homogeneous and isotropic turbulence, while they are different in other type of turbulent flows. The second channel is more intermittent and acts more like a scalar, especially on small scales. Besides, we find a novel mechanism of hindered even inverse energy cascade, which could be attributed to the second-channel helicity flux with large amplitude.Helicity exists in many natural phenomena, such as hurricanes, tornadoes, and rotating "supercell" thunderstorms in the atmosphere, Langmuir circulation in the ocean, and  -effect and  -effect in the magnetic field [1,2]. In the past few decades, there have been numerous theoretical and numerical conclusions indicating that helicity could reduce the aerodynamic drag, nonlinearity of Navier-Stokes equations (NSEs), and improve the mixing effectiveness of reactants [1,3]. Helicity, the integral of the scalar product of velocity and vorticity, is the second inviscid invariant of the three-dimensional(3D) NSEs, which indicate that helicity cascade exists in 3D turbulent flows. Recently, a new research has shown that helicity is a conservative quantity even in viscous flows [4,5]. Helicity is a topological variable, which measures the degree of the linkage of the vortex lines in the flow field [6], and consists of linking, twisting and writhing [4].The classical Richardson-Kolmogorov-Onsager picture of 3D turbulence is based on the concept of energy cascade, which ignores the topology of vortices [7]. Theoretically, there are two possibilities describing the dynamical properties of helicity and energy cascades. One is simultaneous energy and helicity cascades toward smaller scales, and the other is a pure helicity cascade with no cascade of energy, leading to broken -5/3 power law solutions in the turbulent magnetohydrodynamical, convective and atmospheric flows [8,9]. While many studies revealed that through direct numerical simulations (DNS) and shell model there exists a transfer of energy and helicity to small scales simultaneously in turbulent flows at a high Reynolds number [8,[10][11][12][13]. In the process of the joint cascade of energy and helicity in helical turbulence, helicity flux is more

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“…It is known that for large-scale energy and helicity injection the Kolmogorov-like scaling (2.5) is observed, implying a recovery of mirror symmetry at small scales, see for example Sahoo et al (2015); Vallefuoco et al (2018) for recent studies about this issue with and without rotation. In order to have strong multi-scale helicity, it is necessary to resort to a power-law injection (Forster et al 1977;Seoud & Vassilicos 2007).…”

Section: )mentioning

confidence: 99%

“…Recent experimental advancements allowed the production of vortex bundles with a different prescribed topology (Kleckner & Irvine 2013) and the combination of shear and helicity has been studied experimentally and numerically (Herbert et al 2012;Qu et al 2018). Concerning the dual energy-helicity cascade, it is widely believed that for the case of NSE in three spatial dimensions forced on a limited range of scales, both energy and helicity cascade forward (Chen et al 2003a,b;Sahoo et al 2015). This is a dual co-directional cascade according to the classification given in Alexakis & Biferale (2018).…”

Section: Introductionmentioning

confidence: 99%

Helicoidal particles in turbulent flows with multi-scale helical injection

2019

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We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier-Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii-iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence.

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Role of helicity for large- and small-scale turbulent fluctuations

Cited by 30 publications

References 41 publications

Energy cascade and intermittency in helically decomposed Navier–Stokes equations

Energy cascade and intermittency in helically decomposed Navier–Stokes equations

Dual channels of helicity cascade in turbulent flows

Helicoidal particles in turbulent flows with multi-scale helical injection

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