On the third moments in helical turbulence

Chkhetiani, О. G.

doi:10.1134/1.567095

Cited by 66 publications

(79 citation statements)

References 11 publications

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“…Three recent works have derived equations for third-order statistics in isotropic helical flows by considering velocity-vorticity correlations [3,4,5]. In this paper, we show that the Kármán-Howarth equation has a counterpart which arises due to parity-violation in isotropic flows and which can be written solely in terms of two-point velocity correlations.…”

Section: Introductionmentioning

confidence: 86%

“…Here, if we make the same assumption as [3], that the main contribution to the time-derivative comes from the linear term with the next order terms not changing in the inertial range, and neglect the right-hand side in the limit as…”

Section: Derivation Of Kh-helical Scaling Lawmentioning

confidence: 99%

“…This equation was derived by Chkhetiani [3] using the dynamics of velocityvorticity correlations. In the present derivation, we have arrived at the conclusion without the need to directly consider vorticity or helicity.…”

Section: Howarth Equationmentioning

confidence: 99%

“…By "mixed" we mean that the symmetry and parity properties are indeterminate. In the isotropic tensor representation then, there are four terms [9,3] …”

Section: The Third-order Correlation Tensormentioning

confidence: 99%

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The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

Kurien

2003

Physica D: Nonlinear Phenomena

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We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the Kármán-Howarth equation, that arises due to lack of mirror-reflection symmetry in isotropic flows. The main equation we obtain is consistent with the results of O. Chkhetiani [JETP, 63, 768, (1996)] and V.S. L'vov et al.[http://xxx.lanl.gov/abs/chao-dyn/9705016, (1997)] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling ex-1 ponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov 1941 prediction for the scaling exponents of velocity structure function.

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Section: Introductionmentioning

confidence: 86%

Section: Derivation Of Kh-helical Scaling Lawmentioning

confidence: 99%

Section: Howarth Equationmentioning

confidence: 99%

“…By "mixed" we mean that the symmetry and parity properties are indeterminate. In the isotropic tensor representation then, there are four terms [9,3] …”

Section: The Third-order Correlation Tensormentioning

confidence: 99%

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The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

Kurien

2003

Physica D: Nonlinear Phenomena

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“…Many flows of geophysical and astrophysical relevance are subject to rotation and stratification and can therefore attain kinetic helicity. Closure calculations (André & Lesieur 1977), direct numerical simulations (Borue & Orszag 1997;Brandenburg & Subramanian 2005a), as well as shell model calculations (Chkhetiani 1996;Ditlevsen & Giuliani 2001a,b;Stepanov et al 2009) show an approximate k −5/3 scaling for the kinetic helicity, suggesting that kinetic helicity too is subject to a forward cascade toward smaller length scales. On the other hand, kinetic helicity is conserved by the quadratic interactions and might therefore play an important role in the inviscid limit.…”

Section: Introductionmentioning

confidence: 99%

Kinetic helicity decay in linearly forced turbulence

Brandenburg

Petrosyan

2012

Astron Nachr

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The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number.

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Kinetic Helicity in the Earth's Atmosphere

Chkhetiani,

Kurgansky

2023

Geophysical Monograph Series

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On the third moments in helical turbulence

Cited by 66 publications

References 11 publications

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

Kinetic helicity decay in linearly forced turbulence

Kinetic Helicity in the Earth's Atmosphere

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