  The two-dimensional ideal fluid and the plasma confined by a strong magnetic
field exhibit an intrinsic tendency to organization due to the inverse spectral
cascade. In the asymptotic states reached at relaxation the turbulence has
vanished and there are only coherent vortical structures. We are interested in
the regime that precedes these ordered flow patterns, in which there still is
turbulence and imperfect but robust structures have emerged. To develop an
analytical description we propose to start from the stationary coherent states
and (in the direction opposite to relaxation) explore the space of
configurations before the extremum of the functional that defines the
structures has been reached. We find necessary to assemble different but
related models: point-like vortices, its field theoretical formulation as
interacting matter and gauge fields, chiral model and surfaces with constant
mean curvature. These models are connected by the similar ability to describe
randomly interacting coherent structures. They derive exactly the same equation
for the asymptotic state (sinh-Poisson equation, confirmed by numerical
calculation of fluid flows). The chiral model, to which one can arrive from
self-duality equation of the field theoretical model for fluid and from
constant mean curvature surface equations, appears to be the suitable
analytical framework. Its solutions, the unitons, aquire dynamics when the
system is not at the extremum of the action. In the present work we provide
arguments that the underlying common nature of these models can be used to
develop an approach to fluid and plasma states of turbulence interacting with
structures.
