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Minimal energy thresholds for sustained turbulent bands in channel flow

Published online by Cambridge University Press:  18 May 2022

E. Parente Open the ORCID record for E. Parente [Opens in a new window] ,
J.-Ch. Robinet Open the ORCID record for J.-Ch. Robinet [Opens in a new window] ,
P. De Palma Open the ORCID record for P. De Palma [Opens in a new window]  and
S. Cherubini Open the ORCID record for S. Cherubini [Opens in a new window]
E. Parente*
Affiliation:
DynFluid - Arts et Métiers Paris, 151 Bd de l'Hôpital, 75013 Paris, France Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Via Re David 200, 70126 Bari, Italy
J.-Ch. Robinet
Affiliation:
DynFluid - Arts et Métiers Paris, 151 Bd de l'Hôpital, 75013 Paris, France
P. De Palma
Affiliation:
Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Via Re David 200, 70126 Bari, Italy
S. Cherubini
Affiliation:
Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Via Re David 200, 70126 Bari, Italy
*
†Email address for correspondence: [email protected]
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Abstract

In this work, nonlinear variational optimization is used for obtaining minimal seeds for the formation of turbulent bands in channel flow. Using nonlinear optimization together with energy bisection, we have found that the minimal energy threshold for obtaining spatially patterned turbulence scales with $Re^{-8.5}$ for $Re>1000$. The minimal seed, which is different to that found in a much smaller domain, is characterized by a spot-like structure surrounded by a low-amplitude large-scale quadrupolar flow filling the whole domain. This minimal-energy perturbation of the laminar flow has dominant wavelengths close to $4$ in the streamwise direction and $1$ in the spanwise direction, and is characterized by a spatial localization increasing with the Reynolds number. At $Re \lesssim 1200$, the minimal seed evolves in time, creating an isolated oblique band, whereas for $Re\gtrsim 1200$, a quasi-spanwise-symmetric evolution is observed, giving rise to two distinct bands. A similar evolution is found also at low $Re$ for non-minimal optimal perturbations. This highlights two different mechanisms of formation of turbulent bands in channel flow, depending on the Reynolds number and initial energy of the perturbation. The selection of one of these two mechanisms appears to be dependent on the probability of decay of the newly created stripe, which increases with time, but decreases with the Reynolds number.

JFM classification

Instability: Nonlinear instability Instability: Shear-flow instability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A18
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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