Hamiltonian vortex models in the theory of turbulence

A closed evolutional equation for the vorticity distribution function is defined, with its solution examined by the Liouville equation for an ensemble of straightline vortex filaments using a Prigogine-Balescu diagram technique. The Liouville equation furnishes a statistical form of the motion of the system of vortex filaments, which interact strongly. The distribution function of small functions and their potential for interaction is examined in terms of Fourier expansion, and matrix elements are determined on the basis of the plane waves. Renormalization of the Green's function takes the collective character of the vortex interaction into account. The method is used to examine the production of information entropy in the evolutionary process.