Forced phase diffusion in a convection experiment

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

“…The stable structures within such a band can be generated by appropriately engineered time histories of the parameters and/or by properly changing the boundary conditions, e. g., the system size. The most intensively investigated examples in this respect are the structures of Taylor vortices [1][2][3][4][5][6][7] in an annulus between concentric cylinders of which the inner one rotates and convective roll patterns in horizontal layers of one-component fluids [1,[8][9][10][11]5] or binary mixtures heated from below [12,13].…”

Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

“…From the figure one may conclude that the group velocity for overall drift is about 1/7 of the phase velocity corresponding to the counterpropagating roll drift. An overall group drift is commonly observed in the literature for patterns subjected to a broken lateral symmetry [17,18,19,21]. On the other hand, the counterpropagating-roll phase drift and the temporally periodic amplitude modulation in the central zone are unexpected, and will require further elucidation.…”

“…Riecke and Paap [48], for example, showed that if q(x) penetrates into the Eckhaus-unstable band, phase drift may occur. In addition, Rehberg et al [18] carried out experiments in which two ramps with opposite slope at the ends of a Rayleigh-Bérnard cell selected two different wavenumber profiles q lef t (x) and q right (x), which can generate a unidirectional phase drift from high q toward low q. The authors explained these experiments with a qualitative model showing that drift will occur whenever there is no overlap between the finite-width selection bands centered on q lef t (x) and q right (x).…”

“…Hartung et al [17], for example, discovered convection patterns with a uniform group drift in a RBC experiment in which both U/D and lateral symmetry were broken due to the temperature-dependence of the viscosity and spatial modulations in the cell height. Rehberg et al [18] showed that two ramps with opposite slope could force uniform phase drift in RBC. Ning et al [19] found traveling vortex waves in a Taylor vortex experiment in which a ramp was created with an axial variation of the annular width.…”

Over two decades of pattern formation, a personal perspective

“…[109] The two ramps selected different wavenumbers, and thus created a wavenumber gradient in the system interior. From the phase-diffusion equation this is expected to lead to a travelling wave of convection rolls, which was indeed observed in the experiment.…”