9.2 Radial evolution of intermittency at high latitude

Recently, Pagel and Balogh (2003

) studied intermittency in the outer heliosphere using Ulysses observations at high heliographic latitude, well within high speed solar wind. In particular, these authors used Castaing distribution Castaing et al. (2001

) to study the Probability Density Functions (PDF) of the fluctuations of magnetic field components. They found that intermittency of small scales fluctuations, within the inertial range, increased with increasing the radial distance from the Sun as a consequence of the growth to larger scales of the inertial range.

As a matter of fact, using the scaling found by Horbury et al. (1996a ) between the transition scale (the inverse of the frequency corresponding to the break-point in the magnetic field spectrum) $T ~ r1.1±0.1 B$ , Pagel and Balogh (2003 ) quantitatively evaluated how the top of the inertial range in their data should shift to larger time scales with increasing heliocentric distance. Moreover, taking into account that inside the inertial range $c2 ~ t- b ===> c2 = at-b$ and that the proposed scaling from Castaing et al. (2001 ) would be $c2 ~ const.(t/T )- b$ , we should expect that for $t = T$ the parameter $c2 = const.$ . Thus, these authors calculated $2 s$ and $2 c$ at different heliocentric distances and made the hypothesis of a similar scaling for $2 s$ and $2 c$ , although this is not assured by the model. Figure 96 reports values of $c2$ and $s2$ vs. distance calculated for the top of the inertial range at that distance using the above procedure. The radial behavior shown in this figure suggests that there is no radial dependence for these parameters for all the three components (indicated by different symbols), as expected if the observed radial increase of intermittency in the inertial range is due to a broadening of the inertial range itself.

Figure 96:

Values of $c2$ (upper panel) and $s2$ (lower panel) vs. heliocentric distance. These values have been calculated for the projected low frequency beginning of the inertial range relative to each distance (see text for details). R, T, and N components are indicated by asterisks, crosses and circles, respectively (adopted from Pagel and Balogh, 2003 , © 2003 American Geophysical Union, reproduced by permission of American Geophysical Union).

They also found that, in the RTN reference system, transverse magnetic field components exhibit less Gaussian behavior with respect to the radial component. This result should be compared with results from similar studies by Marsch and Tu (1994 ) and Bruno et al. (2003b ) who, studying the radial evolution of intermittency in the ecliptic, found that the components transverse to the local magnetic field direction, are the most Gaussian ones. Probably, the above discrepancy depends totally on the reference system adopted in these different studies and it would be desirable to perform a new comparison between high and low latitude intermittency in the mean-field reference system.

Pagel and Balogh (2002 ) focused also on the different intermittent level of magnetic field fluctuations during two fast latitudinal scans which happened to be during solar minimum the first one, and during solar maximum the second one. Their results showed a strong latitudinal dependence but were probably not, or just slightly, affected by radial dependence given the short heliocentric radial variations during these time intervals. They analyzed the anomalous scaling of the third order magnetic field structure functions looking at the value of the parameter $m$ obtained from the best fit performed using the p-model (see Section 8.1). In a previous analysis of the same kind, but focused on the first latitudinal scan, the same authors tested three intermittency models, namely: “lognormal”, “p” and “G-infinity” models. In particular, this last model was an empirical model introduced by Pierrehumbert (1999 ) and Cho et al. (2000 ) and was not intended for turbulent systems. Anyhow, the best fits were obtained with the lognormal and Kolmogorov-p model. These authors concluded that magnetic field components display a very high level of intermittency throughout minimum and maximum phases of solar cycle, and slow wind shows a lower level of intermittency compared with the Alfvénic polar flows. These results do not seem to agree with ecliptic observations (Marsch and Liu, 1993 ; Bruno et al., 2003a ) which showed that fast wind is generally less intermittent than slow wind not only for wind speed and magnetic field magnitude, but also for the components. At this point, since it has been widely recognized that low latitude fast wind collected within corotating streams and fast polar wind share many common turbulence features, they should be expected to have many similarities also as regards intermittency. Thus, it is possible that also in this case the reference system in which the analysis is performed plays some role in determining some of the results regarding the behavior of the components. In any case, further analyses should clarify the reasons for this discrepancy.