Numerical Simulations and Flow Instabilities

Abstract

The theories which have been discussed in Sections 4 and 5 are based on the twoscale separation scheme. The large-scale MHD fields are treated as the reproducible background flow, which is usually assumed to be time-independent or even previously given. The small-scale MHD fields are treated as irreproducible and turbulent fields, which vary randomly in space and time. The nonlinear interactions between different small fields are described by using a Kolmogorov type dimensional analysis. Concerning interactions between small-scale and large-scale fields, only the interactions between large-scale field and the ensemble averages over small-scale fields are considered in these theories (see Section 9). As Roberts and Goldstein (1991) and Zhou and Matthaeus (1990a) pointed out, the major problem with this two-scale separation is that these scale-separated theories disregard the subset of intermediate meso-scale fluctuations and interactions between them. This cannot describe the real solar wind, because the observed power spectra indicate a continuum of fluctuations with no clear dividing line between scales. Futhermore the theoretical models cannot describe the nonlinear interactions completely. For example they cannot describe nonlinear interactions that are non-local in wavenumber space, especially between the large-scale and the small-scale fluctuations, or nonlinear interactions being of anisotropic nature. One important way to deal with these difficult problems is MHD numerical simulations.