Correlations at large scales and the onset of turbulence in the fast solar wind

Abstract

We show that the scaling of structure functions of magnetic and velocity fields in a mostly highly Alfv\'{e}nic fast solar wind stream depends strongly on the joint distribution of the dimensionless measures of cross helicity and residual energy. Already at very low frequencies, fluctuations that are both more balanced (cross helicity $\sim 0$) and equipartitioned (residual energy $\sim 0$) have steep structure functions reminiscent of "turbulent" scalings usually associated with the inertial range. Fluctuations that are magnetically dominated (residual energy $\sim -1$), and so have closely anti-aligned Elsasser-field vectors, or imbalanced (cross helicity $\sim 1$), and so have closely aligned magnetic and velocity vectors, have wide `$1/f$' ranges typical of fast solar wind. We conclude that the strength of nonlinear interactions of individual fluctuations within a stream, diagnosed by the degree of correlation in direction and magnitude of magnetic and velocity fluctuations, determines the extent of the $1/f$ region observed and thus the onset scale for the turbulent cascade.