Transport theory and the WKB approximation for interplanetary MHD fluctuations

An alternative approach, based on a multiple scale analysis, is presented in order to reconcile the traditional WKB approach to the modeling of interplanetary fluctuations in a mildly inhomogeneous large‐scale flow with a more recently developed transport theory. This enables us to compare directly, at a formal level, the inherent structure of the two models. In the case of noninteracting, incompressible (Alfvén) waves, the principle difference between the two models is the presence of leading‐order couplings (called “mixing effects”) in the non‐WKB turbulence model which are absent in a WKB development. Within the context of linearized MHD, two cases have been identified for which the leading order non‐WKB “mixing term” does not vanish at zero wavelength. For these cases the WKB expansion is divergent, whereas the multiple‐scale theory is well behaved. We have thus established that the WKB results are contained within the multiple‐scale theory, but leading order mixing effects, which are likely to have important observational consequences, can never be recovered in the WKB style expansion. Properties of the higher‐order terms in each expansion are also discussed, leading to the conclusion that the non‐WKB hierarchy may be applicable even when the scale separation parameter is not small.