TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Bifurcation to oscillations and chaos in rotating convection Y1 - 1999 ER - TY - JOUR A1 - Demircan, Ayhan 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, rotating fluid layer. Periodic boundary conditions in the horizontal directions and stress-free boundary conditions at the top and bottom are assumed. Y1 - 2000 ER - TY - JOUR A1 - Demircan, Ayhan A1 - Scheel, S. A1 - Seehafer, Norbert T1 - Heteroclinic behavior in rotating Rayleigh-Benard 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. Y1 - 2000 UR - http://link.springer.de/link/service/journals/10051/bibs/0013004/00130765.htm ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Dynamos in rotating and nonrotating convection in the form of asymmetric squares N2 - We study the dynamo properties of asymmetric square patterns in Boussinesq Rayleigh-B'enard convection in a plane horizontal layer. Cases without rotation and with weak rotation about a vertical axis are considered. There exist different types of solutions distinguished by their symmetry, among them such with flows possessing a net helicity and being capable of kinematic dynamo action in the presence as well as in the absence of rotation. In the nonrotating case these flows are, however, always only kinematic, not nonlinear dynamos. Nonlinearly the back-reaction of the magnetic field then forces the solution into the basin of attraction of a roll pattern incapable of dynamo action. But with rotation added parameter regions are found where the Coriolis force counteracts the Lorentz force in such a way that the asymmetric squares are also nonlinear dynamos. Y1 - 2001 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Demircan, Ayhan A1 - Feudel, Fred T1 - Fluid helicity and dynamo effect N2 - Using the incompressible magnetohydrodynamic equations, we have numerically studied the dynamo effect in electrically conducting fluids. The necessary energy input into the system was modeled either by an explicit forcing term in the Navier-Stokes equation or fully selfconsistently by thermal convection in a fluid layer heated from below. If the fluid motion is capable of dynamo action, the dynamo effect appears in the form of a phase transition or bifurcation at some critical strength of the forcing. Both the dynamo bifurcation and subsequent bifurcations that occur when the strength of the forcing is further raised were studied, including the transition to chaotic states. Special attention was paid to the helicity of the flow as well as to the symmetries of the system and symmetry breaking in the bifurcations. The magnetic field tends to be accumulated in special regions of the flow, notably in the vicinity of stagnation points or near the boundaries of convection cells. Y1 - 2001 ER - TY - THES A1 - Demircan, Ayhan T1 - Numerische Untersuchungen zur thermischen Konvektion in einer elektrisch leitenden Flüssigkeitsschicht Y1 - 2001 ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Nonlinear square patterns in Rayleigh-Benard 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. Y1 - 2001 UR - http://www.edpsciences.com/articles/euro/full/2001/02/6376/6376.html ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Dynamo in asymmetric square convection Y1 - 2002 SN - 0309-1929 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Demircan, Ayhan T1 - Dynamo action in cellular convection Y1 - 2003 ER - 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 -