Journal
JOURNAL OF FLUID MECHANICS
Volume 911, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2020.982
Keywords
transition to turbulence; boundary layer stability
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Funding
- Boeing Company through a Strategic Research and Development Relationship Agreement [CT-BA-GTA-1]
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This study extends linear resolvent analysis to account for nonlinear triadic interactions in the frequency domain using the harmonic balance method. By including nonlinearity, the framework identifies worst-case disturbances for laminar-turbulent transition. The calculations reach early stages of the turbulent regime through generation and breakdown of perturbation vortices.
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 -type and -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.
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