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Low-frequency selectivity in flat-plate boundary layer with elliptic leading edge

Wang, Bofu; Mao, Xuerui; Zaki, Tamer A.

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Authors

Bofu Wang

Xuerui Mao

Tamer A. Zaki



Abstract

Linear perturbation analyses of zero-pressure-gradient boundary layers at subcritical Reynolds numbers predict that transient disturbance amplification can take place due to the lift-up mechanism. Upstream, streamwise-elongated vortices yield the largest response per unit of inflow disturbance energy, which takes the form of streamwise elongated streaks. In this work, we compute the linear and also nonlinear inflow disturbances that generate the largest response inside the boundary layer, for flow over a thin flat plate with a slender leading edge. In order to compare our results to earlier linear analyses, we constrain the inlet disturbance to be monochromatic in time, or a single frequency. The boundary layer effectively filters high frequencies, and only low-frequency perturbations induce a strong response downstream. The low-frequency optimal inflow disturbance has a spanwise wavenumber that scales with √ Re, and it consists of streamwise and normal vorticity components: the latter is tilted around the leading edge into the streamwise direction and, further downstream, generates streaks. While none of the computed monochromatic disturbances alone can lead to breakdown to turbulence, secondary instability analyses demonstrate that the streaky base state is unstable. Nonlinear simulations where the inflow disturbance is supplemented with additional white noise undergo secondary instability and breakdown to turbulence.

Citation

Wang, B., Mao, X., & Zaki, T. A. (2019). Low-frequency selectivity in flat-plate boundary layer with elliptic leading edge. Journal of Fluid Mechanics, 866, 239-262. https://doi.org/10.1017/jfm.2019.91

Journal Article Type Article
Acceptance Date Jan 20, 2019
Online Publication Date Mar 6, 2019
Publication Date May 10, 2019
Deposit Date Feb 20, 2019
Publicly Available Date Feb 20, 2019
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 866
Pages 239-262
DOI https://doi.org/10.1017/jfm.2019.91
Keywords Boundary layer; Layer receptivity; Boundary layer stability; Nonlinear instability
Public URL https://nottingham-repository.worktribe.com/output/1571620
Publisher URL https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/lowfrequency-selectivity-in-flatplate-boundary-layer-with-elliptic-leading-edge/5B8F99E32A0CAF1B5292388B001F2D26

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