  Evolving from turbulent states the 2D fluids and the plasmas reach states
characterized by a high degree of order, consisting of few vortices. These
asymptotic states represent a small subset in the space of functions and are
characterised by properties that are difficult to identify in a direct
approach. The field theoretical approach to the dynamics and to the asymptotic
states of fluids and plasmas in 2D provides a considerable extension of the
usual perspective. The present works discusses a series of consequences of the
field theoretical approach, when it is applied to particular problems. The
discussion is developed around known physical problems: the current density
profiles in cylindrical plasma, the density pinch in tokamak and the
concentration of vorticity.
