6 Compressive Turbulence

Interplanetary medium is slightly compressive, magnetic field intensity and proton number density experience fluctuations over all scales and the compression depends on both the scale and the nature of the wind. As a matter of fact, slow wind is generally more compressive than fast wind, as shown in Figure 63

where, following Bavassano et al. (1982a

) and Bruno and Bavassano (1991

), we report the ratio between the power density associated with magnetic field intensity fluctuations and that associated with the fluctuations of the three components. In addition, as already shown by Bavassano et al. (1982a

), this parameter increases with heliocentric distance for both fast and slow wind as shown in the bottom panel, where the ratio between the compression at $0.9 AU$ and that at $0.3 AU$ is generally greater than $1$ . It is also interesting to notice that within the Alfvénic fast wind, the lowest compression is observed in the middle frequency range, roughly between $10- 4-10 -3 Hz$ . On the other hand, this frequency range has already been recognized as the most Alfvénic one, within the inner heliosphere (Bruno et al., 1996 ).

Figure 63:

The first two rows show magnetic field compression (see text for definition) for fast (left column) and slow (right column) wind at $0.3 AU$ (upper row) and $0.9 AU$ (middle row). The bottom panels show the ratio between compression at $0.9 AU$ and compression at $0.3 AU$ . This ratio is generally greater than $1$ for both fast and slow wind.

As a matter of fact, it seems that high Alfvénicity is correlated with low compressibility of the medium (Bruno and Bavassano, 1991

; Klein et al., 1993

; Bruno and Bavassano, 1993

) although compressibility is not the only cause for a low Alfvénicity (Roberts et al., 1991 , 1992 ; Roberts, 1992 ).

The radial dependence of the normalized number density fluctuations $dn/n$ for the inner and outer heliosphere were studied by Grappin et al. (1990 ) and Roberts et al. (1987b ) for the hourly frequency range, but no clear radial trend emerged from these studies. However, interesting enough, Grappin et al. (1990 ) found that values of $- e$ were closely associated with enhancements of $dn/n$ on scales longer than $1 h$ .

On the other hand, a spectral analysis of proton number density, magnetic field intensity, and proton temperature performed by Marsch and Tu (1990b ) and Tu et al. (1991 ) in the inner heliosphere, separately for fast and slow wind (see Figure 64 ), showed that normalized spectra of the above parameters within slow wind were only marginally dependent on the radial distance. On the contrary, within fast wind, magnetic field and proton density normalized spectra showed not only a clear radial dependence but also similar level of power for $k < 4 .10-4 km s- 1$ . For larger $k$ these spectra show a flattening that becomes steeper for increasing distance, as was already found by Bavassano et al. (1982b ) for magnetic field intensity. Normalized temperature spectra does not suffer any radial dependence neither in slow wind nor in fast wind.

Spectral index is around $- 5/3$ for all the spectra in slow wind while, fast wind spectral index is around $- 5/3$ for $k < 4 .10 -4 km -1$ and slightly less steep for larger wave numbers.

Figure 64:

From left to right: normalized spectra of proton temperature (adopted from Tu et al., 1991 ), number density, and magnetic field intensity fluctuations (adopted from Marsch and Tu, 1990b , © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union) Different lines refer to different heliocentric distances for both slow and fast wind.

6.1 On the nature of compressive Turbulence
6.2 Compressive turbulence in the polar wind
6.3 The effect of compressive phenomena on Alfvénic correlations