Non-linear input/output analysis: application to boundary layer transition

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 maximize 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 Tollmien-Schlichting waves, streaks and their breakdown. We show that nonlinearity plays a critical role in optimizing 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.

arXiv comment30 pages

References in corpus (6)

• Spectral analysis of jet turbulence
• Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow
• Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
• Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets
• A minimal model of self-sustaining turbulence
• Optimal perturbations and transition energy thresholds in boundary layer shear flows

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