Convective versus absolute instability in flow between counterrotating cylinders

Spiral and Taylor vortex fronts and pulses in axial through flow

“…(4.4, 4.5) one has to evaluate the dispersion relation σ(Q) for complex Q [21,24]. To that end we solved the eigenvalue problem (2.28) of the full field equations for complex Q (cf., Sec.…”

Parametric forcing of waves with a nonmonotonic dispersion relation: Domain structures in ferrofluids

“…The dispersion relation becomes non-monotonic when the group velocity changes sign. This is the case in spiral vortex flow between counter-rotating cylinders in certain parameter regimes [18]. However, the parametric forcing of spiral vortex flow has turned out to be non-trivial due to the appearance of Stokes layers [19].…”

Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

“…These boundary conditions are realized in different extended systems, where the pattern amplitude vanishes near lateral boundaries (Zaleski et al 1985;Andereck et al 1986;Mutabazi et al 1990;Tagg et al 1990;Laure & Mutabazi 1994;Tagg 1994;Bot et al 1998;Bot & Mutabazi 2000;Ezersky et al 2001Ezersky et al , 2004Garnier & Chiffaudel 2001;Garnier et al 2002;Lepiller et al 2007). Contrary to the problem with periodic boundary conditions, the group velocity s cannot be removed from the equation since the system has no Galilean invariance.…”

“…However, in a large number of experiments in bounded domains, patterns have a finite length and the perturbations decay near the lateral walls. This is the case, for example, in the rectangular Rayleigh-Bénard convection cell (Kolodner et al 1986); in the pattern of thermo-capillary waves in a laterally heated liquid layer (Garnier & Chiffaudel 2001;Garnier et al 2002); in spiral vortex flow in the Couette-Taylor flow between counter-rotating cylinders (Zaleski et al 1985;Andereck et al 1986;Tagg et al 1990;Tagg 1994;Ezersky et al 2004); in the travelling rolls in a cylindrical annulus with a radial temperature gradient (Lepiller et al 2007); in the travelling inclined vortex flow in the Taylor-Dean system (Mutabazi et al 1990;Laure & Mutabazi 1994;Bot et al 1998;Bot & Mutabazi 2000); and in parametrically excited ripples in viscous fluids (Ezersky et al 2001). To explain the regimes observed in these experiments on pattern formation in bounded flow systems with lateral boundaries, it is necessary to consider the conditions that are more close to experimental situations.…”