Stationarity in Solar Wind Flows

By using single-point measurements in space physics it is possible to study a phenomenon only as a function of time. This means that we cannot have direct access to information about spatial variations of a measured quantity. However, the investigation of the properties of turbulence and of related phenomena in the solar wind widely makes use of an approximation frequently adopted in hydrodynamics under certain conditions, the so-called Taylor hypothesis; indeed, the solar wind flow has a bulk velocity along the radial direction which is much higher than the velocity of a single turbulent eddy embedded in the main flow. This implies that the time of evolution of the turbulent features is longer than the transit time of the flow through the spacecraft position, so that the turbulent field can be considered frozen into the solar wind flow. This assumption allows one to easily associate time variations with spatial variations and stationarity to homogeneity. We have investigated, applying criteria for weak stationarity to Ulysses magnetic field data in different solar wind regimes, at which timescale and under which conditions the hypothesis of stationarity, and then of homogeneity, of turbulence in the solar wind is well justified. We extend the conclusions of previous studies by Matthaeus and Goldstein to different parameter ranges in the solar wind. We conclude that the stationarity assumption in the inertial range of turbulence on timescales of 10 minutes to 1 day is reasonably satisfied in fast and uniform solar wind flows, but that in mixed, interacting fast, and slow solar wind streams the assumption is frequently only marginally valid.