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ARTICLESReynolds number effects on
RayleighTaylor instability with possible
implications for type-Ia supernovaeWILLIAM H. CABOT* AND ANDREW W. COOK*Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, California 94550-9234, USA
*e-mail: [email protected]; [email protected] online: 23 July 2006; doi:10.1038/nphys361Spontaneous mixing of uids at unstably stratiedinterfaces occurs in a wide variety of atmospheric,oceanic, geophysical and astrophysical ows. TheRayleighTaylor instability, a process by which uidsseek to reduce their combined potential energy, playsa key role in all types of fusion. Despite decades ofinvestigation, fundamental questions regarding turbulentRayleighTaylor ow persist, namely: does the ow forgetits initial conditions, is the ow self-similar, what is thescaling constant, and how does mixing inuence thegrowth rate? Here, we show results from a large directnumerical simulation addressing such questions. Thesimulated ow reaches a Reynolds number of 32,000, farexceeding that of all previous RayleighTaylor simulations.We nd that the scaling constant cannot be found bytting a curve to the width of the mixing layer (as iscommon practice) but can be obtained by recourse tothe similarity equation for the expansion rate of theturbulent region. Moreover, the ratio of kinetic energy toreleased potential energy is not constant, but exhibits aweak Reynolds number dependence, which might haveprofound consequences for ame propagation models intype-Ia supernova simulations.RayleighTaylor instabilities (RTIs) arise from baroclinic
generation of vorticity at a perturbed interface subject
to acceleration in a direction opposite the mean density
gradient1,2. RTI plays a crucial role in all known forms of fusion,
whether the connement be magnetic3, inertial4,5 or gravitational6.
Regarding gravitational fusion, much work over recent years points
to RayleighTaylor-driven turbulence as the dominant acceleration
mechanism for thermonuclear ames in type-Ia supernovae7.In
addition to producing many intermediate-mass elements, type-Ia
supernovae serve as standard candles for measuring the rate of
expansion of the universe. They begin as carbonoxygen white
dwarfs, which accrete mass from a companion star. When the
mass of the white dwarf reaches the Chandrasekhar limit of 1.4
solar masses, ignition occurs near the centre, thus generating a
thermonuclear ame front. The expansion of ashes behind the
front causes the ame to become RayleighTaylor unstable as it
propagates outwards.A major diculty in supernova modelling is the need to cover
the vast dynamic range associated with high Reynolds number
turbulence. The thermonuclear ame varies in thickness, from
104 to 1 cm (ref. 8), whereas...