### 2.5 The inhomogeneous case

Equations (16) refer to the standard homogeneous and incompressible MHD. Of course, the solar wind
is inhomogeneous and compressible and the energy transfer equations can be as complicated as we want by
modeling all possible physical effects like, for example, the wind expansion or the inhomogeneous large-scale
magnetic field. A set of equations for the cross-correlation functions of both Elsässer fluctuations have
been developed independently by Marsch and Tu (1989), Zhou and Matthaeus (1990), Oughton and
Matthaeus (1992), and Tu and Marsch (1990a), following Marsch and Mangeney (1987) (see review
by Tu and Marsch, 1996), and are based on some rather strong assumptions: i) a two-scale
separation, and ii) small-scale fluctuations are represented as a kind of stochastic process (Tu
and Marsch, 1996). These equations look quite complicated, and just a comparison based on
order-of-magnitude estimates can be made between them and solar wind observations (Tu and
Marsch, 1996).