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Nonlinear optimal perturbation of turbulent channel flow as a precursor of extreme events

Published online by Cambridge University Press:  29 August 2023

N. Ciola Open the ORCID record for N. Ciola [Opens in a new window] ,
P. De Palma ,
J.-C. Robinet Open the ORCID record for J.-C. Robinet [Opens in a new window]  and
S. Cherubini
N. Ciola*
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy DynFluid, Arts et Métiers Paris/CNAM, 151 Bd de l'Hôpital, 75013 Paris, France
P. De Palma
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
J.-C. Robinet
Affiliation:
DynFluid, Arts et Métiers Paris/CNAM, 151 Bd de l'Hôpital, 75013 Paris, France
S. Cherubini
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
*
†Email address for correspondence: n.ciola@phd.poliba.it
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Abstract

This work aims at studying the mechanisms behind the occurrence of extreme dissipation events in a channel flow, identifying nonlinear optimal perturbations as potential precursors of these events. Nonlinear optimal perturbations with respect to a generic turbulent instantaneous snapshot are computed for the first time using a direct-adjoint algorithm in the channel flow at $Re_{\tau }\approx 180$. The resulting initial perturbation displays the upstream tilting characteristic of Orr's mechanism and is positioned along the interfaces between two opposite-sign velocity streaks of the pre-existing turbulent field. Such a perturbation induces a sudden breakdown of the pre-existing structures and a heavier tail in the dissipation probability density function distribution. Different mechanisms are at play during this process: the high shear present at the interface between coherent low- and high-momentum regions is exploited to break down the larger structures and drive energy to small scales. This energy cascade is fed by an enhanced lift-up effect that produces intense streaks near the wall. It is found that the optimal perturbation grows exponentially during the first phase of its evolution reflecting the existence of a secondary modal instability of the streaks. To corroborate the results, the conditional spatiotemporal proper orthogonal decomposition (POD) analysis of Hack & Schimdt (J. Fluid Mech., vol. 907, 2021, A9) is performed both in the perturbed and in the unperturbed flow, showing a clear agreement between the two cases and with the reference study. Thus, the optimal perturbation at initial time can be considered as a precursor of extreme events.

JFM classification

Turbulent Flows: Turbulent Flows Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A6
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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