Stability of hexagonal patterns in Benard-Marangoni convection
Hexagonal patterns in Benard-Marangoni (BM) convection are studied within the framework of amplitude equations. Near threshold they can be described with Ginzburg-Landau equations that include spatial quadratic terms. The planform selection problem between hexagons and rolls is investigated by explicitly calculating the coefficients of the Ginzburg-Landau equations in terms of the parameters of the fluid. The results are compared with previous studies and with recent experiments. In particular, steady hexagons that arise near onset can become unstable as a result of long-wave instabilities. Within weakly nonlinear theory, a two-dimensional phase equation for long-wave perturbations is derived. This equation allows us to find stability regions for hexagon patterns in BM convection.
- Sponsoring Organization:
- (US)
- OSTI ID:
- 40203437
- Journal Information:
- Physical Review E, Vol. 63, Issue 6; Other Information: DOI: 10.1103/PhysRevE.63.066307; Othernumber: PLEEE8000063000006066307000001; 093102PRE; PBD: Jun 2001; ISSN 1063-651X
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
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