von Kármán-Howarth equation for three-dimensional two-fluid plasmas.

  title={von K{\'a}rm{\'a}n-Howarth equation for three-dimensional two-fluid plasmas.},
  author={Nahuel Andr{\'e}s and Pablo D. Mininni and Pablo A. Dmitruk and Daniel O. G{\'o}mez},
  journal={Physical review. E},
  volume={93 6},
We derive the von Kármán-Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifths" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate… 

Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas.

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Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence.

The exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.

Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence.

An exact law is derived for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamic turbulence, without the assumption of isotropy to provide an accurate means to estimate the energy cascade rate over a broad range of scales.

Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence.

The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived and the role of the background magnetic field B_{0} is highlighted and a comparison with the incompressible MHD (IMHD) model is discussed.

Local and global properties of energy transfer in models of plasma turbulence

The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov–Maxwell

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We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and

Electron-scale reduced fluid models with gyroviscous effects

Reduced fluid models for collisionless plasmas including electron inertia and finite Larmor radius corrections are derived for scales ranging from the ion to the electron gyroradii. Based either on

D ec 2 02 1 Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence : a link between fluid cascade and instabilities

We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new

Incompressive Energy Transfer in the Earth’s Magnetosheath: Magnetospheric Multiscale Observations

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Turbulence in space plasmas and beyond

  • S. Galtier
  • Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2018
Most of the visible matter in the Universe is in the form of highly turbulent plasmas. For a long time the turbulent character of astrophysical fluids has been neglected and not well understood. One



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

A derivation in variable dimension of the scaling laws for mixed third-order longitudinal structure and correlation functions for incompressible magnetized flows is given for arbitrary correlation

The third-order law for magnetohydrodynamic turbulence with shear: Numerical investigation

The scaling laws of third-order structure functions for isotropic, homogeneous, and incompressible magnetohydrodynamic (MHD) turbulence relate the observable structure function with the energy

von Kármán-Howarth relationship for helical magnetohydrodynamic flows.

An exact equation is derived for homogeneous isotropic magnetohydrodynamic (MHD) turbulent flows with nonzero helicity, which links the dissipation of magnetic helicity to the third-order correlations involving combinations of the components of the velocity, the magnetic field, and the magnetic potential.

Application of extended self-similarity in turbulence

From Navier-Stokes turbulence numerical simulations we show that for the extended self-similarity (ESS) method it is essential to take the third order structure function taken with the modulus and

Kármán–Howarth theorem for the Lagrangian-averaged Navier–Stokes–alpha model of turbulence

The Lagrangian averaged Navier–Stokes–alpha (LANS-α) model of turbulence is found to possess a Kármán–Howarth (KH) theorem for the dynamics of its second-order autocorrelation functions in

Two-fluid turbulence including electron inertia

We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure and electron inertia.

Dynamical length scales for turbulent magnetized flows

We derive two symmetric global scaling laws for third‐order structure functions of magnetized fluids under the assumptions of full isotropy, homogeneity and incompressibility. The compatibility with

On the third moments in helical turbulence

The evolution of the correlation characteristics in homogeneous helical turbulence is studied. Additional Kármán-Howarth-type equations describing the evolution of the mixed correlation tensor of the

Exact relationship for third-order structure functions in helical flows

  • GómezPolitanoPouquet
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
An exact law for turbulent flows is written for third-order structure functions taking into account the invariance of helicity, a law akin to the so-called "4/5 law" of Kolmogorov, but the alternative relation derived here is written in terms of mixed structure functions involving combinations of differences of all components for both the velocity and vorticity fields.

Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box.

  • K. Yoshimatsu
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
The influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of r from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.