TY  - INPR
A1  - Demircan, Ayhan
A1  - Seehafer, Norbert
T1  - Nonlinear square patterns in Rayleigh-Bénard convection
N2  - We numerically investigate nonlinear asymmetric square patterns in a horizontal convection layer with up-down reflection symmetry. As a novel feature we find the patterns to appear via the skewed varicose instability of rolls. The time-independent nonlinear state is generated by two unstable checkerboard (symmetric square) patterns and their nonlinear interaction. As the bouyancy forces increase, the interacting modes give rise to bifurcations leading to a periodic alternation between a nonequilateral hexagonal pattern and the square pattern or to different kinds of standing oscillations.
T3  - NLD Preprints - 62 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14986
ER  - 
TY  - INPR
A1  - Demircan, Ayhan
A1  - Scheel, Stefan
A1  - Seehafer, Norbert
T1  - Heteroclinic behavior in rotating Rayleigh-Bénard convection
N2  - We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.
T3  - NLD Preprints - 55 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14914
ER  -