Stationarity of Fast and Slow Solar Wind

Theories of turbulence rely on the ability to view physical fields as stationary random variables and to relate ensemble and time averages through the ergodicity assumption. This property is however poorly realized in the solar wind where the power injection mechanisms have large fluctuations over long periods due to solar rotation and to the solar cycle. The question of stationarity of the statistical quantities like velocity or magnetic field thus has to be addressed, but in-depth studies of stationarity have been few till now. We show in this presentation that, in periods of quiet sun, slow and fast winds cannot be considered as coming from a single stationary time series, even at second order (weak\/ stationarity). This implies that second-order quantities, like spectra or correlation functions, computed over intervals spanning periods of both types of wind, become a mix that cannot be related to the individual properties of these two different physical systems. As the initial forcing mechanisms have different power in the two cases, the combined time series cannot be viewed as coming from a unique stationary turbulent system. The situation is even worse when looking at higher order statistics or intermittency, which can be contaminated by the transition zones between the different types of wind and thus show an apparently higher intermittency than is present in each independent type of wind. Statistical analyses must thus be performed by looking at the different periods of wind separately, as they correspond to different turbulent systems with different initial forcing and power injections.