The Yaglom law in the expanding solar wind

We study the Yaglom law, which relates the mixed third-order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two-scale expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind, two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Els¨asser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecraft, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom’s third-order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.