“…Subsequent observational studies indicated that at magnetohydrodynamic (MHD) scales there are at least two distinct types of fluctuation and that the wave-like energy may be a minor component Bieber et al, 1996;Milano et al, 2004;Dasso et al, 2005;Horbury et al, 2005Horbury et al, , 2008Podesta, 2009;Osman and Horbury, 2009;Narita et al, 2010]. This encouraged development of more complete transport theories for the energy-containing range quantities [e.g., Tu and Marsch, 1993;Matthaeus et al, 1994Matthaeus et al, , 1996Matthaeus et al, , 1999Matthaeus et al, , 2004Zank et al, 1996;Smith et al, 2001Smith et al, , 2006Isenberg et al, 2003Isenberg et al, , 2010aIsenberg, 2005;Breech et al, 2005Breech et al, , 2008Yokoi and Hamba, 2007;Usmanov and Goldstein, 2010;Ng et al, 2010], in which turbulence properties are built in, contrasting with WKB theory, in which the waves are noninteracting at leading order. The agreement between observations made from 0.3 to 80 AU and numerical solutions to these models has also improved, with reasonable accord achieved for the radial evolution of the energy, cross helicity (H c ), and correlation length of the fluctuations and also for the proton temperature.…”