ON LONG-LIVED VORTICES IN 2-D VISCOUS FLOWS, MOST PROBABLE STATES OF INVISCID 2-D FLOWS AND A SOLITON EQUATION

This paper considers, in contraposition to the most probable states of quasi-inviscid theories, the status of the vorticity(omega)-streamfunction(psi) relations satisfied by the long-lived vortices observed in some numerical simulations of decaying two-dimensional turbulence and in experiments in stratified fluids. For the case omega=-Delta psi=sinh psi, the circular solutions can be expressed in terms of the IIIrd Painleve transcendent and dipolar solutions can be constructed by means of a Backlund transform.