X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Brandenburg  (4)
  • UB Potsdam  (4)
  • 1995-1999  (4)
  • Braun, Robert  (4)
  • 1
    Book
    Book
    The route to chaos for a two-dimensional externally driven flow (1998)
    Potsdam : NLD
    Details
    UID:
    gbv_083083340
    Format: 7 S. , graph. Darst.
    Series Statement: Preprint NLD 046
    Content: 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.
    Additional Edition: Online-Ausg. Braun, Robert, 1969 - The route to chaos for a two-dimensional externally driven flow Potsdam : NLD, 1998
    Language: English
    Author information: Braun, Robert 1969-
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Book
    UB Potsdam get availability status
  • 2
    Online Resource
    Online Resource
    The route to chaos for a two-dimensional externally driven flow (1998)
    Potsdam : NLD
    Details
    UID:
    gbv_642383332
    Format: Online-Ressource (PDF-Datei: 7 S., 2.242 kB) , graph. Darst.
    Edition: [2007] Online-Ausg
    Series Statement: Preprint NLD 046
    Content: 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.
    Note: Online-Ausg.
    Additional Edition: Erscheint auch als Druck-Ausgabe Braun, Robert, 1969 - The route to chaos for a two-dimensional externally driven flow Potsdam : NLD, 1998
    Language: English
    URN: urn:nbn:de:kobv:517-opus-14717
    URL: Volltext
    URL: Volltext
    Author information: Braun, Robert 1969-
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Online Resource
    Online Access
    UB Potsdam
  • 3
    Online Resource
    Online Resource
    Bifurcations and chaos in an array of forced vortices (1997)
    Potsdam : NLD
    Details
    UID:
    gbv_642376522
    Format: Online-Ressource (PDF-Datei: 7 Bl., 2.155 kB) , graph. Darst.
    Edition: [2007] Online-Ausg
    Series Statement: Preprint NLD 037
    Content: 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.
    Note: Online-Ausg.
    Additional Edition: Erscheint auch als Druck-Ausgabe Braun, Robert, 1969 - Bifurcations and chaos in an array of forced vortices Potsdam : NLD, 1997
    Language: English
    URN: urn:nbn:de:kobv:517-opus-14564
    URL: Volltext
    URL: Volltext
    Author information: Braun, Robert 1969-
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Online Resource
    Online Access
    UB Potsdam
  • 4
    Book
    Book
    Bifurcations and chaos in an array of forced vortices (1997)
    Potsdam : NLD
    Details
    UID:
    gbv_230265642
    Format: 7 Bl. , graph. Darst. , 30 cm
    Series Statement: Preprint NLD 037
    Content: 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.
    Additional Edition: Erscheint auch als Online-Ausgabe Braun, Robert, 1969 - Bifurcations and chaos in an array of forced vortices Potsdam : NLD, 1997
    Language: English
    Author information: Braun, Robert 1969-
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Book
    UB Potsdam get availability status
Nothing or not found what you are looking for? Please check your search query or use the Interlibrary Loan Search.
Close ⊗
This website uses cookies and the analysis tool Matomo. Further information can be found on the KOBV privacy pages