## 2 Equations and Phenomenology

In this section, we present the basic equations that are used to describe charged fluid flows, and the
basic phenomenology of low-frequency turbulence. Readers interested in examining closely this subject can
refer to the very wide literature on the subject of turbulence in fluid flows, as for example the
recent books by, e.g., Pope (2000), McComb (1990), Frisch (1995) or many others, and the less
known literature on MHD flows (Biskamp, 1993; Boyd and Sanderson, 2003; Biskamp, 2003).
Plasma is seen as a continuous collisional medium so that all quantities are functions of space
and time . Apart for the required quasi-neutrality, the basic assumption of MHD is that
fields fluctuate on the same time and length scale as the plasma variables, say and
( and are, respectively, the wave number and the frequency of the fields,
while and are the hydrodynamic time and length scale, respectively). Since the
plasma is treated as a single fluid, we have to take the slow rates of ions. A simple analysis
shows also that the electrostatic force and the displacement current can be neglected in the
non-relativistic approximation. Then, MHD equations can be derived as shown in the following
sections.