| Comparison
of Experimental and Simulated Mixing Rates
Rayleigh-Taylor instabilities result when a heavy fluid is
supported by a less dense fluid. Gravity causes the heavier
liquid to form “fluid fingers” that flow down
into the lighter liquid, causing mixing and turbulence. Many
natural phenomena, from boiling water to weather inversions
to supernovae, show this kind of behavior, which is why numerical
simulation of Rayleigh-Taylor instabilities is an important
field of research.
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| Figure
4 Cross-sectional plots showing density
on a common rainbow color scale. The pure light fluid
is colored blue and the pure heavy fluid is red. Yellow
and green represent various levels of microscopic mixing.
The ratio of extreme density values is 3.3:1. (Right)
Shown is a higher slice in the z direction. (Upper) FRONTIER.
(Lower) TVD. The simulations are shown at comparable penetration
distances, but at different times. The density contrast
for the TVD simulation has been reduced by about 50% because
of mass diffusion. |
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George et al. conducted a Rayleigh-Taylor mixing rate simulation
with an acceleration rate falling within the range of experiments.
The simulation used the high-resolution front-tracking code
FRONTIER to prevent interfacial mass diffusion. The results
support the assertion that the lower acceleration rate found
in untracked simulations such as total variation diminishing
(TVD) is caused, at least to a large extent, by a reduced
buoyancy force due to numerical interfacial mass diffusion
(Figure 4). Quantitative evidence includes results from a
time-dependent Atwood number analysis of the diffusive simulation,
which yields a renormalized mixing rate coefficient for the
diffusive simulation in agreement with experiment. The main
result is that all values of the acceleration rate 
(theory, experiment, and simulation) are consistent if the
diffusive calculation of
is renormalized to account for mass diffusion.
INVESTIGATORS
J. Glimm, E. George, X.-L. Li, A. Marchese, and Z.-L. Xu,
State University of New York, Stony Brook.
PUBLICATION
E. George, J. Glimm, X.-L. Li, A. Marchese, and Z.-L. Xu,
“A comparison of experimental, theoretical, and numerical
simulation Rayleigh-Taylor mixing rates,” PNAS 99,
2587 (2002).
URL
http://www.ams.sunysb.edu/~shock/FTdoc/FTmain.html |
