Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

Details Numerical study of pattern formation following a convective instability in non-Boussinesq fluids Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

1992-07-10

arxiv.org/abs/cond-mat/9207011v1

Phys. Rev. A 46, R4483 (1992)

Physics

Condensed Matter

9 pages, report FSU-SCRI-92-66

Scientific paper

10.1103/PhysRevA.46.R4483

We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.

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