ON VARIATIONAL-PRINCIPLES FOR COHERENT VORTEX STRUCTURES

Different approaches are discussed of variational principles character izing coherent vortex structures in two-dimensional flows. Turbulent f lows seem to form ordered structures in the large scales of the motion and the self-organization principle predicts asymptotic states realiz ing an extremal value of the energy or a minimum of enstrophy. On the other hand the small scales take care of the increase of entropy, and asymptotic results can be obtained by applying the theory of equilibri um statistical mechanics.