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Nonlinear input/output analysis: application to boundary layer transition

Published online by Cambridge University Press:  26 January 2021

Georgios Rigas Open the ORCID record for Georgios Rigas [Opens in a new window] ,
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window]  and
Tim Colonius
Georgios Rigas*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA91125, USA
Denis Sipp
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190Meudon, France
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA91125, USA
*
Email address for correspondence: g.rigas@imperial.ac.uk
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Abstract

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximise the drag are calculated using a gradient-based ascent algorithm. By including nonlinearity in the analysis, the proposed frequency-domain framework identifies the worst-case disturbances for laminar-turbulent transition. We demonstrate the framework on a flat-plate boundary layer by considering three-dimensional spanwise-periodic perturbations triggered by a few optimal forcing modes of finite amplitude. Two types of volumetric forcing are considered, one corresponding to a single frequency/spanwise wavenumber pair, and a multi-harmonic where a harmonic frequency and wavenumber are also added. Depending on the forcing strategy, we recover a range of transition scenarios associated with $K$-type and $H$-type mechanisms, including oblique and planar Tollmien–Schlichting waves, streaks and their breakdown. We show that nonlinearity plays a critical role in optimising growth by combining and redistributing energy between the linear mechanisms and the higher perturbation harmonics. With a very limited range of frequencies and wavenumbers, the calculations appear to reach the early stages of the turbulent regime through the generation and breakdown of hairpin and quasi-streamwise staggered vortices.

JFM classification

Instability: Transition to turbulence Boundary Layers: Boundary layer stability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

Present address: Department of Aeronautics, Imperial College London, London SW7 2AZ, UK.

References

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