Maximization of vortex entropy as an organizing principle in intermittent, decaying, two-dimensional turbulence.

Attempts to apply methods of statistical thermodynamics to turbulent flows have usually been based on wave number decomposition of an Eulerian velocity field. ' Intermittency, which involves spatially localized phenomena and hence phase correlations, is notoriously difficult to treat in this way. An essential feature of turbulence is the randomization of positions of fluid elements, in the sense of increasing configuration entropy. In two-dimensional (2D) flow at very large Reynolds number, the total energy and the circulation of each fluid element are nearly conserved quantities. Accordingly, Onsager based an alternative statistical approach on an idealization of Lagrangian fluid elements as point vortices. Montgomery employed this approach to describe time-averaged properties of early numerical simulations of 2D turbulence, without reference to intermittency. In recent years, direct numerical simulation has been applied to decaying, incompressible, 2D turbulence obeying Navier-Stokes and related equations of motion at higher resolution and over longer time intervals; the results furnish detailed information about the localized vortex structures which embody intermittent behavior. I will show that discrete-vortex statistics, when extended to incorporate time dependence, can account for several of the features observed in such simulations, namely the presence and predominant form of eddies, and some gross features of the structure function or energy spectrum. I extend earlier research (e.g. , Refs. 9 and 10) by emphasizing fundamentally thermodynamic aspects of the evolution. The vorticity evolves according to the Navier-Stokes equation