Matthaeus, W. H., Zhou, Y., Zank, G. P., & Oughton, S. (1994). Transport theory and the WKB approximation for interplanetary MHD fluctuations. Journal of Geophysical Research, 99(A12), 23421-23430.
Permanent Research Commons link: http://hdl.handle.net/10289/8621
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.