Effects
of small-scale turbulent motions on the filtered velocity
gradient tensor as deduced from holographic PIV measurements
By F. van der Bos*, B. Tao, C. Meneveau, & J. Katz
Department of Mechanical Engineering, The
Johns Hopkins University Baltimore, MD 21218, USA, * current address:
Twente University, Netherlands.
ABSTRACT: The
effects of small-scale motions on the inertial range structure
of turbulence are investigated by considering the dynamics
of the velocity gradient tensor Aij filtered at
scale D. In addition to self-interactions and the filtered
pressure Hessian, the evolution of Aij is determined
by the subgrid-scale stress tensor. As in the so-called Restricted
Euler dynamics, the evolution equations can be simplified by
considering the invariants R and Q of Aij. The effects
of the subgrid-scale stress tensor on R and Q can be quantified
unambiguously by evaluating conditional averages that appear
in the evolution equation for the joint PDF of these invariants.
The required conditional averages are computed from three-dimensional
measurements of fully developed turbulence in a square duct,
at Ret ~ 2,360. The measurements are performed using holographic
particle image velocimetry (Tao et
al. (2000), Phys. Fluids12, p. 941; Tao et
al. (2002), J. Fluid Mech.). The velocity distributions
are spatially filtered in the inertial range using a box filter
at about 30 Kolmogorov scales to separate large from small
scales. The results show that the SGS stresses have significant
effect on the evolution of filtered velocity gradients. In
particular, along the so-called Vieillefosse tail at RD>0
and QD<0, they oppose the formation
of a finite-time singularity that occurs in Restricted Euler
dynamics. Various other trends are quantified in different
parts of the (R,Q) plane. Included are the SGS dissipation
rate of kinetic energy, and the effect of the SGS stress in
modifying the so-called 'discriminant', which is a conserved
quantity in Restricted Euler dynamics. A-priori tests 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 coefficients
be functions of RD and QD.
Phys.
Fluids (2002), 14, p. 2456-2474.
Full
pdf article. -- (©AIP,
see http://ojps.aip.org/phf).
