Nonlinear input/output analysis: application to boundary layer transition. (26th January 2021)

• Record Type: Journal Article
• Authors: Rigas, Georgios; Sipp, Denis; Colonius, Tim
• Is Part Of: Journal of fluid mechanics. Volume 911(2021)
• Publication Date: 2021-01-26
• Subjects: transition to turbulence, -- boundary layer stability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.982
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.