Spectral evolution and cascade constant of solar wind Alfvenic turbulence

The theoretical model of Tu (1988) for the turbulent evolution of solar wind fluctuations assumed the constancy of the ratio alpha(1) between the energy in inward and outward propagating Alfven waves. Here, this model is extended to reflect the observed evolution in the propagation directions of the interplanetary fluctuations. The radial dependence of alpha(1) is determined by direct time domain correlations of the normalized cross helicity. The theoretical results match the observations at least as well as those of the previous, constant alpha(1), model. Measured values of alpha(1) are then used to find the value of the cascade constant that determines the overall level of the energy spectrum. The value of 1.25 for this constant is very close to the value observed in fluid turbulence if it is assumed that the correspondence between fluid and magnetofluid theories should be made for uncorrelated (zero cross helicity) MHD turbulence.