Evolution equations for the vorticity distribution function in the twodimensional case
Abstract
For an ensemble of rectilinear vortex filaments, a closed evolution equation for the vorticity distribution function is derived from the Liouville equation using the PrigozhinBalescu approach. The equation includes a convective Helmholtz operator and a quasilinear elliptic operator of the second order with nonlocal coefficients. The local sign of the dissipative coefficient matrix is determined by the instantaneous vorticity distribution. It is shown that generally over the entire flow region, the evolution involves a monotonic increase in the information entropy and the vorticity distribution tends to become stationary.
 Publication:

PMTF Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki
 Pub Date:
 June 1983
 Bibcode:
 1983PMTF........27G
 Keywords:

 Flow Equations;
 Two Dimensional Flow;
 Vortex Filaments;
 Vorticity Equations;
 Distribution Functions;
 Entropy;
 Liouville Equations;
 Fluid Mechanics and Heat Transfer