Turbulent Flames in Supernovae
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**Session 41 -- Computational Astrophysics II**
*Display presentation, Wednesday, 1, 1994, 9:20-6:30*

## [41.15] Turbulent Flames in Supernovae

*A.M.Khokhlov (UT Austin)*
First results of three-dimensional simulations of a thermonuclear flame in
Type~Ia supernovae are obtained using a new flame-capturing algorithm, and a
PPM hydrodynamical code. In the absence of gravity, the flame is stabilized
with respect to the Landau (1944) instability due to the difference in
the behaviour of convex and concave portions of the perturbed flame front.
The transition to turbulence in supernovae occurs on scales
$\simeq 0.1 - 10$ km in agreement with the non-linear estimate
$\lambda \simeq 2\pi D^2_l/g_{eff}$
based on the Zeldovich (1966) model for a perturbed flame
when the gravity acceleration increases; $D_l$ is the
normal speed of the laminar flame, and $g_{eff}$ is the effective acceleration.

The turbulent flame is mainly spread by
large scale motions driven by the Rayleigh-Taylor instability.
Small scale turbulence facilitates rapid incineration of the fuel
left behind the front.
The turbulent flame speed $D_t$ approaches
$D_t \simeq U'$, where $U'$ is the
root mean square velocity of turbulent motions, when the turbulent flame
forgets initial conditions and reaches a steady state.
The results indicate that in a steady state the
turbulent flame speed should be independent of the normal
laminar flame speed $D_l$.
The three-dimensional results are in sharp contrast with the results of
previous two-dimensional simulations which underestimate flame speed due to
the lack of turbulent cascade directed in three dimensions
from big to small spatial scales.
The work was supported by the NSF grants AST 92-18035 and AST 93-005P.

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