On the cascade processes of Alfven waves in the fast solar wind

We present a numerical study which explores the nonlinear cascade effect associated with Alfven waves in the fast solar wind. The set of one-dimensional, two-fluid equations describing the solar wind and a power spectrum equation for Alfven waves, as first proposed by Tu et al. [1984], are solved simultaneously in a self-consistent manner. Both Kolmogorov and Kraichnan cascade functions, which vary as f(5/2)P(3/2) and f(3)P(2), respectively, are considered, For an Alfven wave spectrum at the coronal base, which is flat in the low-frequency range and has aslope of -1 in the high-frequency range, the Kolmogorov cascade function reproduces the Alfven wave spectrum observed beyond 0.29 AU very well. The Kraichnan cascade function, on the other hand, yields a spectrum that is within the 90% confidence level of the observed values. Both cascade functions yield a gradually accelerating fast solar wind in the inner corona, typical of wave acceleration models. The results of this first solar wind model which describes, in a self-consistent manner, the evolution of the wave spectrum and cascade in the inner corona confirm conclusions reached by earlier studies; namely, that the Kolmogorov process produces a stronger cascade effect than the Kraichnan process and seems more relevant for Alfven waves in the fast solar wind, at least beyond 0.29 AU. The approach shows that Alfven waves, with periods of hours or shorter, undergo an appreciable evolution from the solar surface to 1 AU, thus implying that their spectrum; hence their total energy flux at the Sun cannot be readily predicted from that observed in interplanetary space.