Spontaneous mixing of fluids at unstably stratified interfaces occurs in a wide variety of atmospheric, oceanic, geophysical and astrophysical flows. The Rayleigh–Taylor instability, a process by which fluids seek to reduce their combined potential energy, plays a key role in all types of fusion. Despite decades of investigation, fundamental questions regarding turbulent Rayleigh–Taylor flow persist, namely: does the flow forget its initial conditions, is the flow self-similar, what is the scaling constant, and how does mixing influence the growth rate? Here, we show results from a large direct numerical simulation addressing such questions. The simulated flow reaches a Reynolds number of 32,000, far exceeding that of all previous Rayleigh–Taylor simulations. We find that the scaling constant cannot be found by fitting a curve to the width of the mixing layer (as is common practice) but can be obtained by recourse to the similarity equation for the expansion rate of the turbulent region. Moreover, the ratio of kinetic energy to released potential energy is not constant, but exhibits a weak Reynolds number dependence, which might have profound consequences for flame propagation models in type Ia supernova simulations.
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We wish to thank B. J. Miller, M. L. Welcome and P. L. Williams for assistance with code optimization, and H. R. Childs for help in creating Figs 1 and 6. This work was carried out under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
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Cabot, W., Cook, A. Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae. Nature Phys 2, 562–568 (2006). https://doi.org/10.1038/nphys361
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