Size invariance of the granular Rayleigh-Taylor instability.
The size scaling behavior of the granular Rayleigh-Taylor instability [J. L. Vinningland, Phys. Rev. Lett. 99, 048001 (2007)] is investigated experimentally, numerically, and theoretically. An upper layer of grains displaces a lower gap of air by organizing into dense fingers of falling grains separated by rising bubbles of air. The dependence of these structures on the system and grain sizes is investigated. A spatial measurement of the finger structures is obtained by the Fourier power spectrum of the wave number k. As the size of the grains increases the wave number decreases accordingly which leaves the dimensionless product of wave number and grain diameter, dk, invariant. A theoretical interpretation of the invariance, based on the scaling properties of the model equations, suggests a gradual breakdown of the invariance for grains smaller than approximately 70 microm or greater than approximately 570 microm in diameter.
Vinningland
Jan Ludvig
JL
Advanced Materials and Complex Systems, Department of Physics, University of Oslo, P.0. Box 1048, 0316 Oslo, Norway. janlv@fys.uio.no
Johnsen
Øistein
Ø
Flekkøy
Eirik G
EG
Toussaint
Renaud
R
Måløy
Knut Jørgen
KJ