Isotropic Scaling Features Measured Locally in the Solar Wind Turbulence with Stationary Background Field

The scaling anisotropy is crucial to interpret the nonlinear interactions in solar wind turbulence. Previous observations provide diverse results and the structure function analyses are also reported to be an approach to investigate the scaling anisotropy based on a local magnetic field. However, the determination of the sampling angle with respect to the local background magnetic field requires that the observed time series for the average are time stationary. Whether or not this required time stationarity is compatible with the measurements has not been investigated. Here we utilize the second-order structure function method to study the scaling anisotropy with a time-stationary background field.We analyze 88 fast solar wind intervals each with time durations larger than 2 days measured by WIND spacecraft in the period 2005-2018. We calculate the local magnetic field as the average of the time series B whose time stationarity is fulfilled by our criterion phi smaller than 10 deg (phi is the angle between the two averaged magnetic fields after cutting B into two halves). We find for the first time the isotropic scaling feature of the magnetic-trace structure functions with scaling indices -0.63 pm 0.08 and -0.70 pm 0.04, respectively, with the local magnetic field parallel and perpendicular to the solar wind velocity directions. The scaling for the velocity-trace structure functions is also isotropic and the indices are -0.47 pm 0.10 and -0.51 pm 0.09. We also find that with increasing phi threshold to 90 deg, the scaling index of the magnetic-trace structure function in the parallel direction decreases to -0.81, while the rms of the instantaneous angle between magnetic field and solar wind velocity increases up to 45deg at the timescale 150 s, indicating a mix of perpendicular measurements into parallel ones at large scales.