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Nonlinear input/output analysis: application to boundary layer transition

Rigas, Georgios and Sipp, Denis and Colonius, Tim (2021) Nonlinear input/output analysis: application to boundary layer transition. Journal of Fluid Mechanics, 911 . Art. No. A15. ISSN 0022-1120.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Rigas, Georgios0000-0001-6692-6437
Sipp, Denis0000-0002-2808-3886
Colonius, Tim0000-0003-0326-3909
Alternate Title:Non-linear input/output analysis: application to boundary layer transition
Additional Information:© The Author(s), 2021. Published by Cambridge University Press. Received 24 January 2020; revised 1 November 2020; accepted 2 November 2020. We would like to thank U. Rist for providing the details for the boundary conditions used in the DNS (Rist & Fasel 1995). This work was initiated while D.S. was Visiting Associate at Caltech. G.R. and T.C. also acknowledge the support of the Boeing Company through a Strategic Research and Development Relationship Agreement CT-BA-GTA-1. The authors report no conflict of interest.
Funding AgencyGrant Number
Boeing Company Strategic Research and Development RelationshipCT-BA-GTA-1
Subject Keywords:transition to turbulence, boundary layer stability
Classification Code:JFM classification: Instability: Transition to turbulence; Boundary Layers: Boundary layer stability
Record Number:CaltechAUTHORS:20200311-160934521
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Official Citation:Rigas, G., Sipp, D., & Colonius, T. (2021). Nonlinear input/output analysis: Application to boundary layer transition. Journal of Fluid Mechanics, 911, A15. doi:10.1017/jfm.2020.982
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101872
Deposited By: Tony Diaz
Deposited On:11 Mar 2020 23:13
Last Modified:19 Feb 2021 18:33

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