TY - BOOK A1 - Braun, Robert A1 - Feudel, Fred T1 - Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation T3 - Preprint NLD Y1 - 1996 VL - 29 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Braun, Robert A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and chaos in an array of forced vortices T3 - Preprint NLD Y1 - 1997 SN - 1432-2935 VL - 37 PB - Univ. Potsdam CY - Potsdam ER - TY - JOUR A1 - Braun, Robert A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and chaos in an array of forced vortices Y1 - 1997 ER - TY - THES A1 - Braun, Robert T1 - Bifurkationen und Strukturbildung in hydrodynamischen Systemen Y1 - 1997 ER - TY - BOOK A1 - Braun, Robert A1 - Feudel, Fred A1 - Guzdar, P. T1 - The route to chaos for a two-dimensional externally driven flow : [to appear in Physical Review E] T3 - Preprint NLD Y1 - 1998 SN - 1432-2935 VL - 46 PB - Univ. Potsdam CY - Potsdam ER - TY - JOUR A1 - Braun, Robert A1 - Feudel, Fred A1 - Guzdar, P. T1 - The route to chaos for a two-dimensional externally driven flow Y1 - 1998 ER - TY - JOUR A1 - Witt, Annette A1 - Feudel, Fred A1 - Gebogi, C. A1 - Kurths, Jürgen A1 - Braun, Robert T1 - Tracer dynamics in a flow of driven vortices JF - Preprint NLD Y1 - 1998 SN - 1432-2935 VL - 51 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Braun, Robert A1 - Feudel, Fred A1 - Gebogi, C. A1 - Kurths, Jürgen A1 - Witt, Annette T1 - Tracer dynamics in a flow of driven vortices Y1 - 1999 ER - TY - INPR A1 - Braun, Robert A1 - Feudel, Fred A1 - Guzdar, Parvez T1 - The route to chaos for a two-dimensional externally driven flow N2 - We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario. T3 - NLD Preprints - 46 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14717 ER - TY - INPR A1 - Braun, Robert A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and chaos in an array of forced vortices N2 - We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective. T3 - NLD Preprints - 37 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14564 ER - TY - INPR A1 - Braun, Robert A1 - Feudel, Fred T1 - Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation N2 - We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set. T3 - NLD Preprints - 29 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14099 ER -