Novel Technique to Obtain Spectral Information from Turbulence Data

The well-known second-order structure function is often used to calculate spectral indices and correlation scales. We compare this non-Fourier technique to a similar one, where we calculate partial variances to find the integral of the underlying spectrum as function of frequency. Comparisons are performed with two independently calculated sets of synthetic data. Both techniques work equally well to calculate the spectral index in the inertial range, but the second-order structure function can resolve only a limited range of indices, in contrast to partial variances that can in principle resolve any value. The partial variance technique yields spectral levels, but not directly correlation scales. It can handle significant data gaps without loss of accuracy. We analyse 64-second resolution ACE data in field-aligned coordinates with the partial variance technique. Assuming a composite slab/2D structure for the turbulence, we find that the slab fraction varies significantly (and in a way apparently unrelated to solar activity) over the period 1998 to 2015. However, its mean value is consistent with the results of other authors for other data sets. We also show how the derived slab spectrum and 2D spectrum vary from 1998 to 2015. This work is based on research supported by South African National Research Foundation Grants 80824, 93592 and 96478.