Aerospace Engineering and Mechanics

**Robust large eddy simulation (LES) of turbulence requires accurate
modeling of the small-scale features of the flow, including their interactions
with the larger scales. Formulations based upon optimal estimation of the
evolution of the filtered field minimize the mean-square error associated with
estimating the short-term dynamics of the resolved scales. Optimal formulations
show great promise (Langford and Moser, 1999), since this evolution term
embodies the stochastic nature of the small scales. However, in order for
optimal formulations to be extended to higher Reynolds numbers, the statistical
and structural nature of the acceleration must be documented.**

**To this end, time-resolved particle-image velocimetry measurements are
made in the streamwise-wall-normal plane of turbulent channel flow at Re?=550
and 1734. Temporal and convective derivatives of velocity are computed from
this data in order to evaluate the small-scale behavior of these quantities as
well as of the velocity itself. Instantaneous velocity fields indicate that the
flow is dominated by small-scale vortex cores believed to be associated with
hairpin/hairpin-like vortices. These vortices have been observed in
realizations of the random velocity in other wall turbulence studies. In the
present work, a deterministic "vortex signature" is determined by
conditional averaging techniques. This average signature is consistent with the
hairpin vortex signature defined by Adrian and co-workers. In addition, the
spatial extent of these small-scale vortices appears to remain relatively
constant within the Reynolds-number range studied herein.**

**Instantaneous time-derivative fields are spatially intermittent and are
dominated by strong events that are spatially coincident with the small-scale
vortex cores seen in the associated velocity fields. Stochastic estimation of
the temporal derivative signature associated with the presence of a vortex
core, coupled with Taylor's hypothesis considerations, shows that the
small-scale vortices remain relatively frozen in time, implying that advective
effects dominate the smaller spatial scales of the temporal derivative of
velocity. The bulk convective derivative of velocity (i.e., the temporal
derivative computed in a reference frame traveling at the bulk velocity) is
found to be nearly an order of magnitude smaller than the temporal derivative
of velocity and is mostly associated with the growth of the vortices away from
the wall. Based upon the trends noted in the instantaneous data, scaling of the
temporal and convective derivative statistics is considered to uncover a
consistent Reynolds-number scaling of the statistics involved in optimal LES
subgrid-scale models.**

209 Akerman Hall

2:30-3:30 p.m.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior Secretary, 625-8000.