MODELING RESULTS ON SPATIAL TRANSPORT AND SPECTRAL TRANSFER OF SOLAR-WIND ALFVENIC TURBULENCE

In this paper a set of time stationary transport equations for incompr essible MHD fluctuations in the solar wind is derived from previous ge neral transport equations (Marsch and Tu, 1989; Zhou and Matthaeus, 19 90a), which have been found to give solutions with fast time variation s. The present derivation is based on the assumption that the fluctuat ions are composed of small-scale convected structures and short-wavele ngth Alfven waves. The different contributions of these two types of f luctuations to the total correlation functions can be evaluated by mea ns of temporal and spatial averaging of the correlations over the smal l scales. Two linearly decoupled sets of transport equations then resu lt, which separately describe the spatial evolution of the turbulent e nergies and cross correlations of the structures and waves. For the pr opagating Alfven waves a multiple-scale analysis yields two WKB-type t ransfer equations for the autocorrelation functions expressed in terms of Elsasser velocity fields. For the structures a third additional eq uation is derived, which determines the evolution of the residual ener gy, that is, the difference between the kinetic and magnetic energy of the convected fluctuations. The final set of equations is slowly vary ing in time and thus satisfactory from the point of view of convention al statistical turbulence theory. The nonlinearities are modeled by ca scading flux functions, which are determined by dimensional analysis f ollowing the Kolmogorov phenomenology and based on the time stationari ty assumption. The new equations are consistent with this assumption a nd equivalent to the equations obtained by Tu and Marsch (1993). The p resent derivation aims at clarifying the relations between the general and the time stationary set of transport equations. Consequently, sta tionary equations governing the spatial and spectral evolution of the power frequency spectra e+/- for Alfvenic fluctuations, described in t erms of the two Elsasser variables, are established and integrated num erically. As a first step to study the effects of the nonlinear terms, we neglect the coupling terms related to convected structures. This a pproximation may apply to the fluctuations observed in fast streams ne ar 0.3 AU. We integrate the resulting two coupled transport equations in frequency-distance-space by employing a new technique based on the method of characteristics. Interplanetary parametric decay instabiliti es are also included in the model. The numerical results obtained show that (1) The cascade process which is based on local nonlinear intera ctions in frequency space cannot transport any initial value of the no rmalized cross-helicity from the low-frequency boundary to the higher- frequency range. Cascade processes alone invariably result in dynamic alignment and cause the spectra of e+ as well as e- to steepen at high er frequencies. (2) However, a parametric-decay-like source term can e nforce the normalized cross-helicity to decrease with increasing helio centric distance and can also produce and sustain a flatter part in th e spectrum of e in the high-frequency range. These results are in qual itative agreement with the observations. Research topics which should be dealt with in the future to complete the present preliminary numeri cal work are also pointed out.