Physical aspects of the field-theoretical description of two-dimensional ideal fluids

摘要

The two-dimensional ideal (Euler) fluids can be described by the classicalfields of streamfunction, velocity and vorticity and, in an equivalent manner,by a model of discrete point-like vortices interacting in plane by aself-generated long-range potential. This latter model can be formalized, inthe continuum limit, as a field theory of scalar matter in interaction with agauge field, in the $su(2) $ algebra. This description has already offered theanalytical derivation of the \emph{sinh}-Poisson equation, which was known togovern the stationary coherent structures reached by the Euler fluid atrelaxation. In order this formalism to become a familiar theoretical instrumentit is necessary to have a better understanding of the physical meaning of thevariables and of the operations used by the field theory. Several problems willbe investigated below in this respect.