Decay of magnetohydrodynamic turbulence in the expanding solar wind: WIND observations

We have studied the decay of turbulence in the solar wind. Fluctuations carried by the expanding wind are naturally damped because of flux conservation, slowing down the development of a turbulent cascade. The latter also damps fluctuations but results in plasma heating. We analyzed time series of the velocity and magnetic field (v and B, respectively) obtained by the WIND spacecraft at 1 au. Fluctuations were recast in terms of the Elsasser variables, $ \boldsymbol{z}_\pm =\boldsymbol{v}\pm \boldsymbol{B}/\sqrt{4\pi\rho} $, with ρ being the average density, and their second- and third-order structure functions were used to evaluate the Politano-Pouquet relation, modified to account for the effect of expansion. We find that expansion plays a major role in the Alfvénic stream, those for which z+ ≫ z−. In such a stream, expansion damping and turbulence damping act, respectively, on large and small scales for z+, and also balance each other. Instead, z− is only subject to a weak turbulent damping because expansion is a negligible loss at large scales and a weak source at inertial range scales. These properties are in qualitative agreement with the observed evolution of energy spectra that is described by a double power law separated by a break that sweeps toward lower frequencies for increasing heliocentric distances. However, the data at 1 au indicate that injection by sweeping is not enough to sustain the turbulent cascade. We derived approximate decay laws of energy with distance that suggest possible solutions for the inconsistency: in our analysis, we either overestimated the cascade of z± or missed an additional injection mechanism; for example, velocity shear among streams.