Mean flow in hexagonal convection: stability and nonlinear dynamics
Abstract
Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the framework of coupled Ginzburg-Landau equations. The equations are in particular relevant for non-Boussinesq Rayleigh-B\'enard convection at low Prandtl numbers. The mean flow is found to (1) affect only one of the two long-wave phase modes of the hexagons and (2) suppress the mixing between the two phase modes. As a consequence, for small Prandtl numbers the transverse and the longitudinal phase instability occur in sufficiently distinct parameter regimes that they can be studied separately. Through the formation of penta-hepta defects, they lead to different types of transient disordered states. The results for the dynamics of the penta-hepta defects shed light on the persistence of grain boundaries in such disordered states.
Cite
@article{arxiv.physics/0107058,
title = {Mean flow in hexagonal convection: stability and nonlinear dynamics},
author = {Yuan-nan Young and Hermann Riecke},
journal= {arXiv preprint arXiv:physics/0107058},
year = {2009}
}
Comments
33 pages, 20 figures. For better figures:http://astro.uchicago.edu/~young/hexmeandir