von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions

Politano, H.; Pouquet, A.

doi:10.1103/physreve.57.r21

Cited by 305 publications

(256 citation statements)

References 26 publications

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“…These triple correlations are time dependent, although this is not indicated in the notation here. One can demonstrate that the pressure terms do not contribute to (2.5) (Politano & Pouquet 1998b), as is also the case for hydrodynamics (de Kármán & Howarth 1938).…”

Section: Von Kármán-howarth Equations For Mhdmentioning

confidence: 92%

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

et al. 2012

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AbstractWe argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

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Section: Von Kármán-howarth Equations For Mhdmentioning

confidence: 92%

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

et al. 2012

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“…For K-41 hydrodynamic turbulence for we have the "4/5" law <δv 3 L >∼−4/5L (e.g. Frisch, 1995) determined from the Navier-Stokes equations (for the equivalent relation for isotropic MHD see Politano and Pouquet, 1998). This follows since <δv 3 >/L is the energy transfer rate.…”

Section: Scaling Exponents Mhd Turbulence Models and Similarity Analmentioning

confidence: 92%

Solar cycle dependence of scaling in solar wind fluctuations

Chapman

Hnat

Kiyani

2008

Nonlin. Processes Geophys.

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Abstract. In this review we collate recent results for the statistical scaling properties of fluctuations in the solar wind with a view to synthesizing two descriptions: that of evolving MHD turbulence and that of a scaling signature of coronal origin that passively propagates with the solar wind. The scenario that emerges is that of coexistent signatures which map onto the well known "two component" picture of solar wind magnetic fluctuations. This highlights the need to consider quantities which track Alfvénic fluctuations, and energy and momentum flux densities to obtain a complete description of solar wind fluctuations.

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“…Note that the term involving mixed correlations of the velocity and magnetic fields contains the field B rather than its increment δB -this hints at the nonlocality of the interaction between u and B, which, as explained in §1, is the fundamental feature of MHD turbulence. Equation (2.2) was derived by Chandrasekhar (1951) (see also Politano & Pouquet 1998b). He also found the two other exact laws of MHD turbulence by constructing evolution equations analogous to equation (2.1) for B i B ′ j and u i B ′ j (representing the magnetic-energy and the cross-helicity budgets, respectively).…”

Section: Exact Scaling Laws For Isotropic Mhd Turbulencementioning

confidence: 99%

Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence

2007

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This paper examines the consistency of the exact scaling laws for isotropic MHD turbulence in numerical simulations with large magnetic Prandtl numbers Pm and with Pm = 1. The exact laws are used to elucidate the structure of the magnetic and velocity fields. Despite the linear scaling of certain third-order correlation functions, the situation is not analogous to the case of Kolmogorov turbulence. The magnetic field is adequately described by a model of stripy (folded) field with direction reversals at the resistive scale. At currently available resolutions, the cascade of kinetic energy is short-circuited by the direct exchange of energy between the forcing-scale motions and the stripy magnetic fields. This nonlocal interaction is the defining feature of isotropic MHD turbulence.

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von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions

Cited by 305 publications

References 26 publications

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

Solar cycle dependence of scaling in solar wind fluctuations

Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence

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