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Stochastic modelling of a noise-driven global instability in a turbulent swirling jet

Published online by Cambridge University Press:  06 April 2021

Moritz Sieber Open the ORCID record for Moritz Sieber [Opens in a new window] ,
C. Oliver Paschereit  and
Kilian Oberleithner Open the ORCID record for Kilian Oberleithner [Opens in a new window]
Moritz Sieber*
Affiliation:
Chair of Fluid Dynamics, Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623Berlin, Germany Laboratory for Flow Instabilities and Dynamics, Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623Berlin, Germany
C. Oliver Paschereit
Affiliation:
Chair of Fluid Dynamics, Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623Berlin, Germany
Kilian Oberleithner
Affiliation:
Laboratory for Flow Instabilities and Dynamics, Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623Berlin, Germany
*
†Email address for correspondence: [email protected]
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Abstract

A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics is separated into deterministic contributions representing the global mode and a stochastic contribution representing the intrinsic turbulent forcing. Stochastic models are developed that account for the interaction between the two and allow the determination of the dynamic properties of the flow from stationary data. The deterministic contributions are modelled by an amplitude equation, which describes the oscillatory dynamics of the instability, and in a second approach by a mean-field model, which additionally captures the interaction between the instability and the mean-flow corrections. The stochastic contributions are considered as coloured noise forcing, representing the spectral characteristics of the stochastic turbulent perturbations. The methodology is applied to a turbulent swirling jet with a dominant global mode. Particle image velocimetry measurements are conducted to ensure that the mode is the most dominant coherent structure, and further pressure measurements provide long time series for the model calibration. The supercritical Hopf bifurcation is identified from the linear growth rate of the global mode, and the excellent agreement between measured and estimated statistics suggest that the model captures the relevant dynamics. This work demonstrates that the sole observation of limit-cycle oscillations is not sufficient to determine the stability of turbulent flows, since the stochastic perturbations obscure the actual bifurcation point. However, the proposed separation of deterministic and stochastic contributions in the dynamical model allows the identification of the flow state from stationary measurements.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Turbulent Flows: Turbulence modelling Vortex Flows: Vortex breakdown
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A7
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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