Polymer-induced vortex modification in decaying two-dimensional turbulence

The statistical mechanics of the steady state of a decaying two-dimensional turbulent liquid is extended to the case when the fluid is polymeric. The simple liquid in the rheological fluid is replaced by a vortex gas in a description of the free energy at negative temperatures. The resulting equation of motion must coincide with the inviscid limit of the rheological equation of motion. This gives an expression for the polymeric free energy in terms of the normal stresses. An axisymmetric coherent vortex is discussed and the highly nonlinear equation of motion is addressed qualitatively. The influence of the polymer is to broaden the coherent vortex.