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

Abstract

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