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.

arXiv comment13 pages

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Cited by in corpus (18)

• Cascades and transitions in turbulent flows
• On exact laws in incompressible Hall magnetohydrodynamic turbulence
• Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids
• Spectral transfer and Kármán-Howarth-Monin equations for compressible Hall magnetohydrodynamics
• 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
• Local cascade and dissipation in incompressible Hall magnetohydrodynamic turbulence: the Coarse-Graining approach
• Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: toward linking energy cascade and instabilities
• Statistics of incompressible hydrodynamic turbulence: an alternative approach
• 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
• Determination of energy flux rate in homogeneous ferrohydrodynamic turbulence using two-point statistics
• Energy transfer in simple and active binary fluid turbulence {\bf {-}} a false friend of incompressible MHD turbulence
• Universal turbulent relaxation of fluids and plasmas by the principle of vanishing nonlinear transfers
• Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions
• The role of field correlations on turbulent dissipation
• Rugged magneto-hydrodynamic invariants in weakly collisional plasma turbulence: Two-dimensional hybrid simulation results