Role of cross helicity in magnetohydrodynamic turbulence

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Abstract

Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in imbalanced regions where cross-helicity is non-zero. When averaged over regions of positive and negative cross-helicity, the result is consistent with the simulations of balanced turbulence. An analytical explanation for the obtained results is proposed.

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Spectrum of magnetohydrodynamic turbulence

Stanislav Boldyrev (2005)

We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached, it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of fluid and magnetic-field fluctuations at each scale \(\lambda\) become effectively aligned within the angle \(\phi_{\lambda}\propto \lambda^{1/4}\), which leads to scale-dependent depletion of nonlinear interaction and to the field-perpendicular energy spectrum \(E(k_{\perp})\propto k_{\perp}^{-3/2}\). Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.

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Rapid directional alignment of velocity and magnetic field in magnetohydrodynamic turbulence

W. H. Matthaeus, P. Dmitruk, P. Mininni … (2007)

We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters. This is observed both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between the magnetic field and either pressure gradients or shear-associated kinetic energy gradients. A similar alignment, of velocity and vorticity, occurs in the Navier Stokes fluid case. This may be the most rapid and robust relaxation process in turbulent flows, and leads to a local weakening of the nonlinear terms in the small scale vorticity and current structures where alignment takes place.

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Dynamic Alignment in Driven Magnetohydrodynamic Turbulence

Joanne Mason, Fausto Cattaneo, Stanislav Boldyrev (2006)

Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale \lambda approximately as \theta_\lambda ~ \lambda^{1/4}. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) ~ k^{-3/2} that is observed in numerical experiments of strongly magnetized turbulence.