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Sozialisation
(1998)
Die Habsburgermonarchie
(1998)
Absolutismus in Deutschland
(1998)
Die Käferfauna im Überblick
(1998)
Die romantische Musikästhetik unter besonderer Berücksichtigung der Ansichten von E. T. A. Hoffmann
(1998)
Zum Subjekt emanzipatorischer Projekte : die Aufklärung als geschichtsphilosophisches Konzept
(1998)
Watson, J. R., Die Auschwitz-Galaxy, Reflexionen zur Aufgabe des Denkens; Wien, Turia + Kant, 1998
(1998)
Compressions and extensions
(1998)
Verbreiterte Bemessungsgrundlage und Tarifsenkungspotiential im deutschen Einkommensteuerrecht
(1998)
Verteilung und Fiskus : die Auswirkungen der Einkommensbesteuerung auf die Einkommensverteilung
(1998)
Wirkungen des Menschen auf die Landschaftsentwicklung an der Stadtwüstung Nienover im Solling
(1998)
The route to chaos for a two-dimensional externally driven flow : [to appear in Physical Review E]
(1998)
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.