An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence

Abstract

We propose an alternative formulation for the exact relations in three-dimensional homogeneous turbulence using two-point statistics. Our finding is illustrated with incompressible hydrodynamic, standard and Hall magnetohydrodynamic turbulence. In this formulation, the cascade rate of an inviscid invariant of turbulence can be expressed simply in terms of mixed second-order structure functions. Besides the usual variables like the velocity $\mathbf{u}$, vorticity $\omega$, magnetic field $\mathbf{b}$ and the current $\mathbf{j}$, the vectors $\mathbf{u}\times \mathbf{\omega }$, $\mathbf{u}\times \mathbf{b}$ and $\mathbf{j}\times \mathbf{b}$ are also found to play a key role in the turbulent cascades. The current methodology offers a simple algebraic form which is specially interesting to study anisotropic space plasmas like the solar wind, with in principle a faster statistical convergence than the classical laws written in terms of third-order correlators.

13 pages

References in corpus (3)

• Observation of inertial energy cascade in interplanetary space plasma
• Multiscale nature of the dissipation range in gyrokinetic simulations of Alfvénic turbulence
• On the von Karman-Howarth equations for Hall MHD flows

Cited by in corpus (6)

• Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas
• General exact law of compressible isentropic magnetohydrodynamic flows: theory and spacecraft observations in the solar wind
• Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence
• An in-depth numerical study of exact laws for compressible Hall magnetohydrodynamic turbulence
• Energy transfer, discontinuities and heating in the inner solar wind measured with a weak and local formulation of the Politano-Pouquet law
• The role of field correlations on turbulent dissipation