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  • 1
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    The effects of physical boundaries on oscillatory bifurcation in counterrotating Taylor-Couette flow (2004)
    AIP
    In:  Physics of Fluids, 16 (8). pp. 2757-2762.
    Details
    Publication Date: 2017-01-02
    Description: The results of an experimental study on the bifurcation structure of oscillatory modes in counterrotating Taylor–Couette flow with stationary end plates are presented. It is shown that the cylinder length L acts as an important geometric control parameter of the system. As a result of a supercritical Hopf bifurcation it is found that for an aspect ratio Γ=L/d〉16 (d gap width) only spiral vortices appear in basic laminar flow. For Γ〈10.5 spiral vortices are almost entirely replaced by two types of standing waves called SW0 and SWπ as supercritical oscillatory flow. Experimental evidence is presented that the mode exchange between standing waves SW0 and SWπ is governed by underlying Ekman induced vortices which appear as a result of stationary end plates in the flow. In this regime spiral vortices appear only from a sub- or supercritical symmetry breaking bifurcation of the standing waves. Within an “intermediate regime” between 10.5⩽Γ⩽16 spiral vortices are found to be the predominant primary oscillatory flow but small stability intervals of standing waves are also observed. Surprisingly, the experimentally determined critical Reynolds number is found to deviate not more than 2% from the numerical values for all values of aspect ratio even though they are calculated under the assumption of infinite axial length. Moreover, the critical oscillation frequency is also in agreement with the numerical values and is independent from Γ.
    Type: Article , PeerReviewed
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  • 2
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    A Nonlinear Theory for El Niño Bursting (2003)
    AMS (American Meteorological Society)
    In:  Journal of the Atmospheric Sciences, 60 . pp. 152-165.
    Details
    Publication Date: 2018-04-16
    Description: A new mechanism is proposed that explains two key features of the observed El Niño–Southern Oscillation (ENSO) phenomenon—its irregularity and decadal amplitude changes. Using a low-order ENSO model, the authors show that the nonlinearities in the tropical heat budget can lead to bursting behavior characterized by decadal occurrences of strong El Niño events. La Niña events are not affected, a feature that is also seen in ENSO observations. One key result of this analysis is that decadal variability in the Tropics can be generated without invoking extratropical processes or stochastic forcing. The El Niño bursting behavior simulated by the low-order ENSO model can be understood in terms of the concept of homoclinic and heteroclinic connections. It is shown that this new model for ENSO amplitude modulations and irregularity, although difficult to prove, might explain some features of ENSO dynamics seen in more complex climate models and the observations.
    Type: Article , PeerReviewed
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  • 3
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    Convective and absolut instabilites in counterrotating spiral-Poiseuille flow (2004)
    Springer
    In:  Theoretical and Computational Fluid Dynamics, 18 (2/4). pp. 97-103.
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    Publication Date: 2018-01-19
    Type: Article , NonPeerReviewed
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  • 4
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    Transient dynamics at the onset of Tailor vortices (2003)
    Cambridge University Press
    In:  Journal of Fluid Mechanics, 476 . pp. 335-343.
    Details
    Publication Date: 2019-01-15
    Description: The effect of boundary conditions on the ‘critical dynamics’ at the onset of Taylor vortices is investigated in a combined numerical and experimental study. Numerical calculations of Navier–Stokes equations with ‘stress-free’ boundary conditions show that the Landau amplitude equation provides a good model of the transient dynamics. However, this rapidly breaks down when the ‘no-slip’ condition is approached. Apparent ‘critical’ behaviour observed in experiments is shown to have a surprising dependence on the length of the system.
    Type: Article , PeerReviewed
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  • 5
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    An Organizing Center for Thermohaline Excitability (2004)
    AMS (American Meteorological Society)
    In:  Journal of Physical Oceanography, 34 (12). pp. 2756-2760.
    Details
    Publication Date: 2020-08-04
    Description: The bifurcation behavior of a conceptual heat–salt oscillator model is analyzed by means of numerical continuation methods. A global (homoclinic) bifurcation acts as an organizing center for the dynamics of the simplified convective model. It originates from a codimension-2 bifurcation in an extended parameter space. Comparison with earlier work by Cessi shows that the intriguing stochastic thermohaline excitability can be understood from the bifurcation structure of the model. It is argued that global bifurcations may play a crucial role in determining long-term variability of the thermohaline circulation.
    Type: Article , PeerReviewed
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  • 6
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    Taylor-Couette flow with independently rotating end plates (2004)
    Springer
    In:  Theoretical and Computational Fluid Dynamics, 18 (2-4). pp. 129-136.
    Details
    Publication Date: 2018-01-19
    Type: Article , NonPeerReviewed
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  • 7
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    Chaos from Hopf Bifurcation in a fluid flow experiment (2004)
    American Physical Society (APS)
    In:  Physical Review E, 70 (046209).
    Details
    Publication Date: 2019-02-27
    Description: Results of an experimental study of a Hopf bifurcation with broken translation symmetry that organizes chaotic homoclinic dynamics from a T2 torus in a fluid flow as a direct consequence of physical boundaries are presented. It is shown that the central features of the theory of Hopf bifurcation in O(2)-symmetric systems where the translation symmetry is broken are robust and are appropriate to describe the appearance of modulated waves, homoclinic bifurcation, Takens-Bogdanov point, and chaotic dynamics in a fluid flow experiment.
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  • 8
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    Standing waves in flow between finite counter-rotations cylinders (2003)
    American Physical Society (APS)
    In:  Physical Review E, 68 (056308).
    Details
    Publication Date: 2017-01-03
    Description: Experimental evidence for standing waves resulting from a supercritical Hopf bifurcation that appears as the first pattern-forming instability in counterrotating Taylor-Couette flow is presented. Depending on the aspect ratio two different types of standing waves, denoted as SW0 and SWp, could be observed. Both modes have an azimuthal wave number m51 but differ in symmetry. While for SWp , a spatiotemporal glide-reflection symmetry could be found, SW0 is purely spatial reflection symmetric. The transition between the two modes is found to be organized in a cusp bifurcation unfolded by variations of the aspect ratio. The ‘‘classical’’ spiral vortex flow appears in this control parameter regime only as a result of a secondary steady bifurcation from SW0. This transition is found to be either subcritical or supercritical. The experimentally observed bifurcation structure has been predicted by theory of Hopf bifurcation to spiral vortex flow in finite counterrotating Taylor-Couette systems.
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