  The objective of this paper is to unravel any relations that may exist
between turbulent shear flows and statistical mechanics, through a detailed
numerical 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 the
streamwise direction (x) and evolves from a plane vortex sheet in the direction
normal to it (y) in a periodic-in-x domain with period L. The connections to
statistical mechanics are explored by revisiting, via extensive computer
simulations, an appropriate initial value problem for a finite but large
collection of (N) point vortices of same strength (\gamma) and sign
constituting a 'vortex gas'. Such connections may be expected to be meaningful
as hydrodynamics, since the flow associated with the vortex gas is known to
provide weak solutions of the Euler equation. Over ten different initial
conditions classes are investigated using simulations involving up to 10^4
vortices, with ensemble averages evaluated over up to 10^3 realizations and
integration over 10^4 L/(\Delta U) (where \Delta U is the velocity differential
across the layer, given by N\gamma/L). (see PDF for complete abstract)
