  We investigate two-dimensional turbulence within the Instanton formalism
which determines the most probable field in a stochastic classical field theory
starting from the Martin-Siggia-Rose path integral. We perform an approximate
analysis of these equations based on a variational ansatz using elliptical
vortices. The result are evolution equations for the positions and the shapes
of the vortices. We solve these ordinary differential equations numerically.
The extremal action for the two-point statistics is determined by the merging
of two elliptical vortices. We discuss the relationship of this dynamical
system to the inverse cascade process of two-dimensional turbulence.
