Long-wavelength instability of coherent structures in plane Couette flow.
We study the stability of coherent structures in plane Couette flow against long-wavelength perturbations in wide domains that cover several pairs of coherent structures. For one and two pairs of vortices, the states retain the stability properties of the small domains, but for three pairs new unstable modes are found. They are shown to be connected to bifurcations that break the translational symmetry and drive the coherent structures from the spanwise extended state to a modulated one that is a precursor to spanwise localized states. Tracking the stability of the orbits as functions of the spanwise wave length reveals a rich variety of additional bifurcations.
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany.
Konstantin
K
Melnikov
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany and Max Planck Institut für Dynamik und Selbstorganisation, D-37077 Göttingen, Germany.
Tobias
T
Kreilos
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany and J. M. Burgerscentrum, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands.
Bruno
B
Eckhardt