ON THE STRUCTURE OF PHASE-SPACE, HAMILTONIAN VARIABLES AND STATISTICAL APPROACH TO THE DESCRIPTION OF 2-DIMENSIONAL HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS

The peculiarities of the Hamiltonian description of 2D hydrodynamics and magnetohydrodynamics are discussed in connection with recent attempts to construct a thermodynamical picture for 2D turbulence. The unconstrained Hamiltonian variables are displayed in both cases and the role of topology of the flow in tentative statistical equilibria is discussed. As a by-product the Clebsch-type variables for 2D magnetohydrodynamics are obtained describing flows with initial zero vorticity.