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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Print: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2012005459
pages 399-409

RAYLEIGH−TAYLOR INSTABILITY IN TWO-FLUID AND STRATIFIED MEDIA

Sergey N. Yakovenko
Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Institutskaya Street, 4/1, Novosibirsk 630090, Russia

ABSTRACT

Evolution of the two-fluid interface is studied by direct simulations of Navier−Stokes and volume-fraction equations. To capture surface tension, the continuum surface force model is used. Tests of Rayleigh−Taylor instability demonstrate that the average of spike and bubble amplitudes has an initial exponential growth, corresponding to a linear instability stage with the constant growth rate. Evolution of this rate shows that both viscosity and surface tension result in damping of the instability development, in agreement with measurements and theory. For real fluids, good prediction is obtained at both linear instability and nonlinear stages. If the density difference across the interface is not large, the nonlinear instability stage reveals clear effects of a Kelvin−Helmholtz instability leading to typical mushroomlike structures. The similar convective structures are observed in direct simulations of a stably stratified flow above the obstacle when overturning and breaking internal waves produce unstable layers with strong density gradients. If the density difference is large (e.g., at the water−air interface), the heavier fluid penetrates deeply into the lighter one, forming high columns. The surface tension omission gives spurious distortion of the interface, then its fragmentation. The vortex-sheet method underestimates the instability growth rate. Application of the continuum surface force model leads to the correct interface evolution within the experiment's data scatter.


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