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Recovery of the inherent dynamics of noise-driven amplifier flows

Published online by Cambridge University Press:  16 May 2016

Juan Guzmán Iñigo ,
Denis Sipp  and
Peter J. Schmid
Juan Guzmán Iñigo*
Affiliation:
ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon, France
Denis Sipp
Affiliation:
ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. The spectrum of the identified model compares well with the results reported in literature for the full-order system. Yet the comparison appears to be only qualitative, due to the poor robustness properties of eigenvalue spectra in noise-amplifier flows. We therefore advocate the use of the frequency response between the upstream sensor and the flow dynamics, which is revealed to be a robust quantity. The frequency response is validated against full-order computations and compares well with a local spatial stability analysis.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer stability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 130 - 145
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Copyright
© 2016 Cambridge University Press 

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