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Abstract
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)