The cross-helicity effect on cascade processes in MHD turbulence

Abstract

The cross helicity H = 〈 v · b 〉 characterizes the level of correlation between pulsations of the magnetic field b and the velocity field v . In the ideal three-dimensional magnetic hydrodynamics, it is the integral of motion alongside with the total energy E T = E v + E b , E v = , and E b = . The third integral of motion is the magnetic helicity; but within the framework of this study, we consider the fields in which the average magnetic helicity is close to zero and, thus, it is not considered here. The representation about the developed turbulence as a random process makes it possible to expect that, if there are no special reasons, the developed conductingfluid turbulence (the MHD turbulence) should be characterized by a low cross-helicity level. Exactly such a situation is usually considered. Interest in cross helicity arose after highly correlated pulsations of velocity and magnetic field were found in the solar wind [1]. Analysis of the energy and helicity evolution in a freely degenerating MHD turbulence showed that the helicity decays more slowly than the energy; hence, the degree of correlation of fields v and b determined by the correlation coefficient C = H/E T can increase in time for the free degeneration [2]. By itself, MHD turbulence gives the possibility of developing various scenarios. The specificity of the conducting-fluid hydrodynamics is the possibility of occurrence of Alfven waves; it is assumed they play a key role in the turbulent cascade, which leads to the Iroshnikov‐Kraichnan spectral law E b ( k ) ~ E v ( k ) ~ k –3/2 [3, 4]. In the calculations on the mesh ( 512 3 ) [5], it was shown that no Kraichnan‐Iroshnikov spectrum arises in the noncorrelated turbulence without an external field, and the turbulence with the spectrum close to E b ( k ) ~ v 2 2