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The objective of this paper is to unravel any relations that may existbetween turbulent shear flows and statistical mechanics, through a detailednumerical investigation in the simplest case where both can be well defined.The shear flow considered for the purpose is the 2D temporal mixing layer,which is a time-dependent flow that is statistically homogeneous in thestreamwise direction (x) and evolves from a plane vortex sheet in the directionnormal to it (y) in a periodic-in-x domain with period L. The connections tostatistical mechanics are explored by revisiting, via extensive computersimulations, an appropriate initial value problem for a finite but largecollection of (N) point vortices of same strength (\gamma) and signconstituting a 'vortex gas'. Such connections may be expected to be meaningfulas hydrodynamics, since the flow associated with the vortex gas is known toprovide weak solutions of the Euler equation. Over ten different initialconditions classes are investigated using simulations involving up to 10^4vortices, with ensemble averages evaluated over up to 10^3 realizations andintegration over 10^4 L/(\Delta U) (where \Delta U is the velocity differentialacross the layer, given by N\gamma/L). (see PDF for complete abstract)

The Turbulent 'Mixing' Layer as a Problem in the Non-equilibrium Statistical Mechanics of a Vortex Gas