David H. Porter, Paul Woodward, and Sarah Anderson

University of Minnesota &

Army High Performance Computing Research
Center, Minneapolis, MN

Annick Pouquet

Observatoire de la Cote D'Azur, Nice, France

**Methodology:** The PPM gas dynamics code was used to simulate the
development and self-similar decay of the compressible turbulence which results
from the stirring of a gas with smooth velocity perturbations of fairly large
amplitude (Mach 1 rms velocities). Periodic boundary conditions and cubic
uniform grids of 512 and 1024 computational zones on a side were used. These
very fine grids, in fact, the largest ever employed in any fluid dynamical
simulation, were used in order to resolve features in the turbulent flow which
are influenced neither by the periodic boundary conditions nor by viscosity.
PPM approximates the inviscid Euler equations, and therefore viscous effects,
which occur due to numerical viscosity, are minimal over a large range of
length and time scales in these flows. In order to study the coherent
structures of the turbulence in the "Kolmogorov inertial range," the simulation
data was filtered in order to average over the small scale features. The
billion-zone turbulence simulation, was performed through a collaboration with
Silicon Graphics, who built a special hardware configuration for this project,
the first "Challenge Array," in their manufacturing facility in Mountain View,
California.

**Accomplishments: **A detailed data set was obtained from this computer
simulation which describes a true Kolmogorov inertial range flow,
uncontaminated by effects of boundary conditions or viscosity and uninfluenced
by prior assumptions about the character of this turbulence. This data set was
obtained in September, 1993, but analysis and visualization of this data has
required over a year. The first glimpses at the vorticity structures in the
Kolmogorov inertial range indicate that vortex tube structures are much shorter
and much more strongly distorted than in the near dissipation range, the only
range observed in previous computer experiments. With the wide range of scales
in the Kolmogorov range which was produced in this work, strong quantitative
evidence was found indicating that the well-known phenomenon of vortex
stretching is indeed in operation, producing the turbulent cascade.

**Significance:** The phenomenon of compressible fluid turbulence is of
fundamental importance in a wide variety of contexts. It plays a role in the
wakes and boundary layers of aircraft, missiles, and projectiles in flight, in
mixing regions of air and combustible material in reactive flows, in mixing
layers near unstable material interfaces in laser fusion applications, and in
environmental fluid dynamics of atmospheric storms and of fluid mixing in
rivers and estuaries. Improving turbulence models is of fundamental importance
to progress in all these areas of interest.

**Future Plans:** The dynamical evolution of our turbulent flow will be
compared with the evolu-tion predicted by different turbulence closure models,
in particular, the popular *k-epsilon* model. The billion-zone
turbulence simulation will also be carried out further in time in the coming
year. We are also beginning to experiment with continuously driven turbulent
flows.