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

Steep nonlinear global modes in spatially developing media

“…8 Nonlinear extensions of these concepts have only recently been developed, mainly in the context of various one-dimensional evolution models in semi-infinite 9,10 or finite 11 domains. The results compare satisfactorily with numerical simulations and experiments for Taylor-Couette flow 12 and Rayleigh-Bénard convection with throughflow. 13,10 Surprisingly, fully nonlinear soft global modes of the CGL equation varying smoothly over a doubly infinite domain have been shown, 14 by application of Wentzel-Kramers-Brillouin-Jeffreys ͑WKBJ͒ theory, to satisfy a nonlinear saddle point criterion which is formally analogous to its linear counterpart.…”

Spiral vortices and Taylor vortices in the annulus between rotating cylinders and the effect of an axial flow

“…For code validation we compared SPI solutions with experiments [9] and TVF solutions with previous numerical simulations [11] and close to onset also with Ginzburg-Landau results [21]. Furthermore, we compared bifurcation thresholds of the nonlinear SPI and TVF solutions with the respective stability boundaries of the linearized NSE [6,14] obtained by a shooting method that is described in detail in [14].…”

“…We mention here in addition a few, more recent papers on selected topics beyond those listed in Ref. [11]: linear analysis of the competition between shear and centrifugal instability mechanisms [12,13]; linear SPI and TVF fronts and pulses [14]; weakly nonlinear bifurcation analysis of axially extended spiral, ribbon, and mixed vortex states with homogeneous amplitudes [2,15]; theoretical/numerical investigation of the nonlinear pattern selection in the absolutely unstable regime under downstream evolving intensity envelopes [11]; theoretical/numerical analysis of noise-sustained patterns in the convectively unstable regime [16] (related experiments are listed in [11]); analysis of the changes in the noise sensitivity across the convective-absolute stability boundary [17]; measurements of velocity fields by particle image velocimetry [18].…”

“…[11] for a partial and far from complete compilation. We mention here in addition a few, more recent papers on selected topics beyond those listed in Ref.…”

Highly turbulent Taylor-Couette turbulence

“…Similar to RB flow, TC flow undergoes a series of transitions from circular Couette flow to chaos and turbulence with increasing Reynolds number [41]. The flow-state dependence on the rotation frequencies of the inner and outer cylinder in TC flow at low Reynolds numbers has been theoretically, numerically and experimentally well-studied in the last century [1,[42][43][44][45][46]. This is in marked contrast to the turbulent case, for which only very few studies exist, which we will now discuss.…”