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arXiv · 2503.08283

Nonlinear optimals and their role in sustaining turbulence in channel flow

Dario Klingenberg·Rich R. Kerswell
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Abstract

We investigate the energy transfer from the mean profile to velocity fluctuations in channel flow by calculating nonlinear optimal disturbances,i.e. the initial condition of a given finite energy that achieves the highest possible energy growth during a given fixed time horizon. It is found that for a large range of time horizons and initial disturbance energies, the nonlinear optimal exhibits streak spacing and amplitude consistent with DNS at least at Re_tau = 180, which suggests that they isolate the relevant physical mechanisms that sustain turbulence. Moreover, the time horizon necessary for a nonlinear disturbance to outperform a linear optimal is consistent with previous DNS-based estimates using eddy turnover time, which offers a new perspective on how some turbulent time scales are determined.

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Dario Klingenberg, Rich R. Kerswell. 2025-03-11. Nonlinear optimals and their role in sustaining turbulence in channel flow. https://arxiv.org/abs/2503.08283

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