Time-dependent Pattern Formation for Convection in Two Layers of Immiscible Liquids
Sponsored by Missouri Western State University Sponsored by a grant from the National Science Foundation DUE-97-51113
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The proper APA Style reference for this manuscript is:
RENARDY, Y. -. & Stoltz, C. G. (1999). Time-dependent Pattern Formation for Convection in Two Layers of Immiscible Liquids. National Undergraduate Research Clearinghouse, 2. Available online at http://www.webclearinghouse.net/volume/. Retrieved June 27, 2017 .

Time-dependent Pattern Formation for Convection in Two Layers of Immiscible Liquids
YURIKO -. RENARDY & C. G. STOLTZ
VIRGINIA TECH DEPARTMENT OF MATHEMATICS

Sponsored by: YURIKO RENARDY (renardyy@math.vt.edu)
ABSTRACT
A linear and weakly nonlinear stability analysis is performed for specific two-layer systems which have beenexamined experimentally in Degen et al (Phys Rev E 57, 6647 (1998)). For their water/silicone oil system, at the depthfraction where oscillations are predicted, manywavelengths are unstable. The neutral stability curve is rather flat in thisregion, and oscillations begin slightlyabove the critical Rayleigh number. The neutral stability curves for theirFluorinert/silicone oil system show that oscillations aretheoretically predicted in a very narrow parameter range. A 3D Hopf bifurcation on a hexagonal lattice is investigatedfor patterns that arise in extended domains. In bothfluid systems, travelling rolls, wavy rolls of type 1, and oscillating trianglesare stable for most regimes.

Submitted 6/3/99 2:46:54 PM
Last Edited 6/3/99 2:54:53 PM
Converted to New Site 03/09/2009

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