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iTi Conference on Turbulence

iTi 2021: Progress in Turbulence IX pp 153–158Cite as

Identification of a Stochastic Hopf Bifurcation from Stationary Measurement Data of a Turbulent Flow

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Part of the Springer Proceedings in Physics book series (SPPHY,volume 267)

Abstract

The observation of a Hopf bifurcation in fluid dynamics is commonly associated with the occurrence of a global hydrodynamic instability. The increase of a control parameter above a critical value causes a change from a stable to an unstable flow condition. This behaviour is well understood for the occurrence of instabilities in laminar flows. In turbulent flows, however, the occurrence of hydrodynamic instabilities is similarly observed but less clear. The current work examines the use of stochastic models to describe the supercritical Hopf bifurcation of the global mode in a turbulent swirling jet. The consideration of the interaction between the global mode and the stochastic turbulent perturbations allows a consistent description of the experimental observations. This opens up extensive possibilities for describing and interpreting the occurrence of hydrodynamic instabilities in turbulent flows.

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References

  1. J. T. Stuart, On the non-linear mechanics of hydrodynamic stability. Journal of Fluid Mechanics 4.1 (1958), pp. 1–21. issn: 0022-1120. https://doi.org/10.1017/S0022112058000276

  2. A. K. M. F. Hussain, W. C. Reynolds, The mechanics of an organized wave in turbulent shear flow. J. Fluid Mechanics 41.02 (1970), p. 241. issn: 0022-1120. https://doi.org/10.1017/S0022112070000605

  3. Kilian Oberleithner, Moritz Sieber, Christian Navid Nayeri, Christian Oliver Paschereit, Christoph Petz, Hans-Christian Hege, Bernd R. Noack, and I. Wygnanski. “Threedimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction”. In: Journal of Fluid Mechanics 679 (2011), pp. 383–414. issn: 0022-1120. https://doi.org/10.1017/jfm.2011.141

  4. Jens S. Müller, Moritz Sieber, Ivan Litvinov, Sergey Shtork, Sergey Alekseenko, and Kilian Oberleithner. “Prediction of vortex precession in the draft tube of a model hydro turbine using mean field stability theory and stochastic modelling”. In: 30th Symposium on Hydraulic Machinery and Systems 2020.Lausanne, Switzerland, 2020

    Google Scholar 

  5. Rudolf Friedrich, Joachim Peinke, Muhammad Sahimi, andReza Rahimi Tabar, M. “Approaching complexity by stochastic methods: From biological systems to turbulence”. In: Physics Reports 506.5 (2011), pp. 87–162. issn: 03701573. doi: https://doi.org/10.1016/j.physrep.2011.05.003

  6. Nicolas Noiray and Bruno Schuermans. “Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors”. In: International Journal of Non-Linear Mechanics 50 (2013), pp. 152–163. issn: 00207462. doi: https://doi.org/10.1016/j.ijnonlinmec.2012.11.008

  7. Moritz Sieber, Christian Oliver Paschereit, and Kilian Oberleithner. “Stochastic modelling of a noise driven global instability in a turbulent swirling jet”. In: Journal of Fluid Mechanics in press (2020). url: https://arxiv.org/abs/ 2007.07555

    Google Scholar 

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Authors and Affiliations

  1. Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, 10623, Berlin, Germany

    Moritz Sieber & Kilian Oberleithner

  2. Chair of Fluid Dynamics, Technische Universität Berlin, 10623, Berlin, Germany

    Moritz Sieber & Christian Oliver Paschereit

Authors
  1. Moritz Sieber
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  2. Christian Oliver Paschereit
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  3. Kilian Oberleithner
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Corresponding author

Correspondence to Moritz Sieber .

Editor information

Editors and Affiliations

  1. Linné FLOW Centre, KTH Engineering Mechanics, Stockholm, Sweden

    Dr. Ramis Örlü

  2. Department of Industrial Engineering, Universita' di Bologna, Forli, Italy

    Prof. Alessandro Talamelli

  3. Institute of Physics, University of Oldenburg, Oldenburg, Niedersachsen, Germany

    Joachim Peinke

  4. Department of Mechanical Engineering, TU Darmstadt, Darmstadt, Germany

    Dr. Martin Oberlack

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Sieber, M., Paschereit, C.O., Oberleithner, K. (2021). Identification of a Stochastic Hopf Bifurcation from Stationary Measurement Data of a Turbulent Flow. In: Örlü, R., Talamelli, A., Peinke, J., Oberlack, M. (eds) Progress in Turbulence IX. iTi 2021. Springer Proceedings in Physics, vol 267. Springer, Cham. https://doi.org/10.1007/978-3-030-80716-0_20

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