Field theoretical methods applied to fluid and plasma problems 
The 2D Euler fluid 
The ideal (nondissipative) twodimensional fluid shows at relaxation from a turbulent state the formation of a coherent pattern of flow. It consists of two vortices of opposite signs (a dipole) and this state is stable. This evolution has been well confirmed by numerical simulations and it was found that the streamfunction verifies the sinhPoisson equation. This is an exactly integrable equation, which indicates a deep and exceptional stucture. The fact that the ideal fluid can reach such a state is strange and suggests some fundamental order. The classical approaches, based on conservation equations, are less efficient in exploring this aspects. The field theoretical method is the appropriate framework: it identifies the states as extrema of an action functional. 

Field theory for the Euler equation 

Liouville equation and the snake of density in tokamak 
The "snake of density" is a phenomenon still not understood: around the magnetic surface q=1 in tokamak a perturbation of density (that may be generated by a pellet) evolves by concentration into a localized formation that has 3D helical shape, regular, stable i.e. resisting to sawteeth longer than expected. The same process takes place with heavy impurities and even with current density. 

Ringtype vorticity distribution 

Comment on conditions of application of Field Theoretical models to plasma and fluid problems 
The Field theoretical formulation can be characterized as very powerful: they dispose of an analytical apparatus that has been developed for decades and has been confronted with deep and complex problems. On the other hand, they are easily applied to identify stable structures as action functional extrema but the equations of motion are in general as complicated as those of the standard fluid/plasma approaches. With one eception, by far the most interesting one: the selfduality. It seems that the nature chooses selfduality as the asymptotic state of any evolution. We examine several field theoretical frameworks that seem adequate for plasma/fluid problems. For an important "caveat emptor" see below. 

Fluids, Field Theory and Constant Mean Curvature surfaces 
A presentation on the connection fluids/surfaces 
Turbulence of unitons 
Structures in turbulence, chiral model and unitons 
The statistical theory of point like vortices is described by a Field Theory with mixed spinors ChernSimons gauge field and long range, Coulombian, interaction. At selfduality the model can be mapped onto a chiral model and further it is equivalent with the Constant Mean Curvature surfaces. We try to pull back from the common asymptotic (identically identified by all these formulations) to include turbulence. 

Attempts to formulate a Field Theoretical model for plasma in strong magnetic field and for the planetary atmosphere 
A model equation proposed for these physical systems with short range of interaction 
The plasma in strong magnetic field and the planetay atmosphere have intrinsic lengths: the Larmor radius and respectively the Rossby radius. This makes a fundamental difference relative to the Field Theoretical formulation for the Euler fluid. For the latter, there is no intrinsic length (conformal invariance). The first idea is to introduce a mass to the photon of the ChernSimons gauge field (without however introducing the Maxwell term since we do not expect short range coherency). This mass (inverse Larmor/Rossby lengths) can result from the equivalent of a Higgs phenomenon, i.e. involving a particular selfinteraction of the matter field. But then, the model (NonAbelian, Chern Simons, self interaction of order 6) leads to an equation that has NO real solutions. If we want to keep a similarity with the sinhPoisson equation we must modify the Bogomolnyi procedure. We have done this, in a way which does not have any physical justification except our desire to keep close to the Euler model. Then we obtain an equation. This equation has been largely ignored or rejected for the reason stated above: it is not derived as a consistent Field Theory but it is created when we decided to modify the analytical path toward SelfDuality of the Euler FT model. The system, in any case, would have lost the selfduality and a residual energy should have to remain. We have applied this equation to the tropical cyclone and to magnetically confined plasma. Strangely enough, it works. A text on this derivation. We have formulated clearly our CAVEAT, above. 
