Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability

Szprynger, A.; Lücke, M.

doi:10.1103/physreve.67.046301

Cited by 5 publications

(3 citation statements)

References 27 publications

(56 reference statements)

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“…Clearly, in the upper panel for ε = 0.102 the Taylor vortex pattern fills the whole cell, and one is in the absolutely unstable regime. The pattern selection in this regime and near the transition was studied numerically in [68,69,272,390].…”

Section: Fronts and Noise-sustained Structures In Convective Systems ...mentioning

confidence: 99%

“…The effect of noise on convective systems has recently been studied systematically for the CGL equation by Proctor et al [358], who map out the full phase diagram (see also [272,390]). In line with our discussion of the behavior of fronts in the CGL equation in sections 2.11.5 and 2.11.6, the behavior as a function of the control parameter ε depends strongly on whether or not the state selected by the front is unstable to the Benjamin-Feir instability.…”

Section: Fronts and Noise-sustained Structures In Convective Systems ...mentioning

confidence: 99%

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Front propagation into unstable states

2003

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This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially localized perturbations spread into an unstable state according to the linear dynamical equations obtained by linearizing the fully nonlinear equations about the unstable state. This allows us to give a precise definition of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is larger than v*. In addition, this approach allows us to clarify many aspects of the front selection problem, the question whether for a given dynamical equation the front is pulled or pushed. It also is the basis for the universal expressions for the power law rate of approach of the transient velocity v(t) of a pulled front as it converges toward its asymptotic value v*. Almost half of the paper is devoted to reviewing many experimental and theoretical examples of front propagation into unstable states from this unified perspective. The paper also includes short sections on the derivation of the universal power law relaxation behavior of v(t), on the absence of a moving boundary approximation for pulled fronts, on the relation between so-called global modes and front propagation, and on stochastic fronts.Comment: final version with some added references; a single pdf file of the published version is available at http://www.lorentz.leidenuniv.nl/~saarloo

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Section: Fronts and Noise-sustained Structures In Convective Systems ...mentioning

confidence: 99%

Section: Fronts and Noise-sustained Structures In Convective Systems ...mentioning

confidence: 99%

Front propagation into unstable states

2003

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“…Most of the research activities were centered on fronts in the quintic Ginzburg-Landau equation [59,61,62,63,64,65]. One can expect that the front properties are fixed by a strongly nonlinear eigenvalue problem describing a heteroclinic orbit between the two involved states.…”

Section: Frontsmentioning

confidence: 99%

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

Jung

Lücke

2005

Phys. Rev. E

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Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated from below. A finite-difference method is used to solve the full hydrodynamic field equations in a vertical cross section of the layer perpendicular to the convection roll axes. Results are presented for ethanol-water parameters with several strongly negative separation ratios where TW solutions bifurcate subcritically. Fronts and LTWs are compared with each other and similarities and differences are elucidated. Phase propagation out of the quiescent fluid into the convective structure entails a unique selection of the latter while fronts and interfaces where the phase moves into the quiescent state behave differently. Interpretations of various experimental observations are suggested.

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Controlling Couette flow by alternating axial mass flux

Altmeyer

2024

Physics of Fluids

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This paper presents numerical simulations of the Taylor vortex flow under the influence of an externally applied alternating axial mass flux (through-flow) in a Taylor–Couette system with axial periodic boundary conditions. Such an axially modulating flow can lead to a significant variation in the onset of primary instabilities. Depending on the system parameters, the effect can be both stabilizing and destabilizing, i.e., shifting the bifurcation threshold to larger or smaller control parameters, respectively. It is found that the system response around the primary instability is sensitive to and critically influenced by an alternating mass flux, particularly the modulation frequency. We show that such an alternating axial flow represents an easily and, more importantly, precisely controllable key parameter to change the nonlinear system response from subcritical to supercritical behavior and vice versa. Furthermore, we observe different parameter regimes with regular and irregular intermittent flow dynamics.

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Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability

Cited by 5 publications

References 27 publications

Front propagation into unstable states

Front propagation into unstable states

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

Controlling Couette flow by alternating axial mass flux

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