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Department of Mechanical Engineering
The Johns Hopkins University
Abstract-
What is the `canonical structure' of turbulent flows
remains an important and multifaceted fundamental question
in turbulence research. One facet relates to typical
local deformations of fluid elements in the neighborhood
of Lagrangian tracers. These deformations are described by
the velocity gradient tensor. Its properties determine, for
instance, if the deformation produces vorticity stretching
along a particular direction (possibly yielding tubular
vortex structures), or to produce structures that are
flattened out in one direction while expanding in the
other two (possibly yielding pancake-like objects).
On the basis of recent three-dimensional measurements in
turbulent duct flow using holographic PIV techniques
(Tao, Katz & Meneveau, J. Fluid Mech. 2002 in press), we
consider the dynamics of the velocity gradient tensor
filtered at inertial-range scales. In addition to
self-interactions and the filtered pressure Hessian, the
evolution of the filtered velocity gradient tensor is
determined by the subgrid-scale stress tensor. As in
so-called Restricted Euler dynamics, the evolution
equations can be simplified by considering two invariants
R and Q. The effects of the subgrid-scale stress tensor
on them can be quantified unambiguously by evaluating
conditional averages that appear in the evolution equation
for the joint PDF of the invariants. The HPIV
measurements show that the SGS stresses have significant
effects, e.g. along the so-called Vieillefosse tail they
oppose the formation of a finite-time singularity that
occurs in Restricted Euler dynamics. Motivated by
practical modeling needs in the context of large eddy
simulations, we examine the behavior of various closures
for the subgrid stresses. Analysis of the Smagorinsky,
nonlinear, and mixed models show that all reproduce the
real SGS stress effect along the Vieillefosse tail, but
that they fail in several other regions. An attempt is
made to optimize the mixed model by letting the two model
coefficients be functions of the two invariants R and Q.
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