ABSTRACT
This chapter discusses the starting equations for a number of specific types of hydrodynamic perturbations. It considers mainly small-scale perturbations. The chapter deals with the perturbations in a plasma flow with an inhomogeneous velocity profile. It also discusses the dispersion relations for the inertialess perturbations in such a plasma flow and non-linear regime of the entropy waves. The chapter shows that the set of non-linear equations for the entropy waves, as well as that of linear equations, is autonomic. It provides the dispersion relation for the inertialess perturbations allowing for the heat transfer, the finiteness of the longitudinal electron heat conductivity and the ion longitudinal motion. The chapter also provides expressions for the viscosity tensor components 𝜋𝛼𝛽 in the reference frame for which one of the axes is directed along the magnetic field. Therefore, it is clear, that the Alfven perturbations in an inhomogeneous plasma are characterized by the crossed-field drift velocity corresponding to the incompressible plasma motion.
