Spatial and temporal resonances in a periodically forced hydrodynamic system

Marqués, Francisco; Lopez, Juan M.

doi:10.1016/s0167-2789(99)00172-4

Cited by 27 publications

(26 citation statements)

References 24 publications

(42 reference statements)

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“…Although this forcing stabilizes both axisymmetric and non-axisymmetric modes, there are windows in parameter space where the onset of instability is to spiral modes via a Neimark-Sacker bifurcation (a Hopf bifurcation from a periodic orbit). Marques & Lopez (2000) showed that in these windows strong resonances between the Neimark-Sacker frequency ω s and the forcing frequency ω f occur, motivating the recent experiments by Sinha et al (2006) who studied the complex nonlinear dynamics subsequent to the Neimark-Sacker bifurcation. Nevertheless, their results contained additional frequencies which could not be identified and were attributed to background noise.…”

Section: Transition To Complex Spatio-temporal Dynamicsmentioning

confidence: 83%

“…The spiral modes predicted by the Floquet analysis of Marques & Lopez (2000), from now on referred to as Mode 1 (M1), bifurcate supercritically from the oscillating basic state (2.3) in a Neimark-Sacker bifurcation. They are characterized by their axial and azimuthal wavenumbers (k, n) which define a constant spiral angle β = tan −1 (−n/k).…”

Section: Onset Of Instabilitymentioning

confidence: 98%

“…In this case, the time-periodic basic state bifurcates to a quasi-periodic torus featuring the forcing frequency, ω f , and the frequency of the spiral mode, ω s . These windows of parameter space were investigated by Marques & Lopez (2000) using Floquet analysis to identify the presence of several strong resonances, i.e. ω s /ω f = p/q with q 6 4.…”

Section: Introductionmentioning

confidence: 99%

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Stability control and catastrophic transition in a forced Taylor–Couette system

et al. 2007

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Harmonic axial motion of the inner cylinder in the Taylor–Couette system can efficiently shift the onset of instability to larger inner cylinder rotation rates. However, once instability has set in, a rapid sequence of symmetry-breaking bifurcations results in complex spatio-temporal dynamics even for very low post-critical values of the rotation rate. Using spectral computations, we present a detailed study of this sudden transition, shedding light on the nature of the complex flows observed in recent laboratory experiments. In particular, it is shown that these bifurcations are responsible for some of the experimentally observed frequencies which had been attributed to background noise. Movies are available with the online version of the paper.

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Section: Transition To Complex Spatio-temporal Dynamicsmentioning

confidence: 83%

Section: Onset Of Instabilitymentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Stability control and catastrophic transition in a forced Taylor–Couette system

et al. 2007

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“…A key contribution of their work was the prediction of regions of complex spatio-temporal instabilities that give rise to the dynamics within this window. Marques & Lopez (2000) focused on these narrow windows in parameter space and discovered strong temporal resonances as well as competition between various spatial modes that were simultaneously excited. An excitation diagram illustrating the critical surface for the bifurcation, and the strong resonances to be expected, was presented.…”

Section: Introductionmentioning

confidence: 99%

Experimental study of a Neimark–Sacker bifurcation in axially forced Taylor–Couette flow

2006

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A variation of the classical Taylor–Couette system is studied where, with the outer cylinder stationary, the inner cylinder rotates at constant angular velocity while executing harmonic oscillations in the axial direction. Experiments reveal a Hopf (Neimark–Sacker) bifurcation from a limit cycle to a torus. Alternating bands of frequency-locked and quasi-periodic flow are observed and identified. Power spectral plots and (delay reconstructed) Poincaré maps are used to characterize the temporal dynamics. Results are presented on the rotation number variation across parameter space, the shape and growth of frequency-locked resonance horns, and the spatial development of the flow considerably beyond the primary transition surface.

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“…Heaton (2008) complemented their analyses by assessing the importance of non-modal effects, and showed their relevance at moderate and large Re z ∼ 10 2 -10 4 . Other recent studies concern rotation of the outer cylinder (Meseguer & Marques 2002), absolute/convective instabilities (Altmeyer, Hoffmann & Lücke 2011), supercritical states (Hwang & Yang 2004), time-periodic flow (Marques & Lopez 2000), additional radial flow (e.g. Martinand, Serre & Lueptow 2009) and so on.…”

Section: Taylor-couette-poiseuille Flowmentioning

confidence: 99%

Temporal stability of eccentric Taylor–Couette–Poiseuille flow

2013

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The combined effects of axial flow and eccentricity on the temporal stability properties of the Taylor-Couette system are investigated using a pseudospectral method. Eccentricity is found to stabilize the Couette flow regardless of axial advection intensity. As the axial Reynolds number Re z is increased for any fixed eccentricity e 0.7, the critical mode switches from deformed toroidal Taylor vortices to helical structures with an increasing number of waves, and with helicity opposed to the innercylinder rotation. For a wide-gap configuration of radius ratio η = 0.5, increasing axial advection has a stabilizing effect for low Re z , then a weak destabilizing effect for high enough Re z . Centrifugal effects are always destabilizing, but axial shear is responsible for the dominance of helical modes of increasing azimuthal complexity. The modes localize in the converging gap region, and the energy concentrates increasingly into axial motion for larger Re z . Critical quantities are also computed for a small-gap case, and similar trends are observed, even though no destabilizing effect of advection is observed within the range of Re z considered. Comparison with the experiment of Coney & Mobbs (Proc. Inst. Mech. Engrs, vol. 184 Pt 3L, 1969-70, pp. 10-17) for η = 0.89 shows good agreement, despite small discrepancies attributed to finite length effects.

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Spatial and temporal resonances in a periodically forced hydrodynamic system

Cited by 27 publications

References 24 publications

Stability control and catastrophic transition in a forced Taylor–Couette system

Stability control and catastrophic transition in a forced Taylor–Couette system

Experimental study of a Neimark–Sacker bifurcation in axially forced Taylor–Couette flow

Temporal stability of eccentric Taylor–Couette–Poiseuille flow

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