Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer

Minjiang Gong, Chengwang Xiong*, Xuerui Mao, Liang Cheng, Shi Ping Wang, A. Man Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The essence of sub-critical transition of oscillatory boundary-layer flows is the non-modal growth of finite-amplitude disturbances. The current understanding of the mechanisms of the orderly and bypass transitions of oscillatory boundary-layer flows is limited. The present study adopts optimisation approaches to predict the maximum energy amplification of two- and three-dimensional perturbations in response to the optimal initial disturbance with or without external forcing. A series of direct numerical simulations are also performed to compare with the results obtained from the stability analyses. In particular, the optimal initial perturbation similar to a Tollmien-Schlichting (T-S) wave yields the largest transient growth under the combined effects of the Orr mechanism and inflectional point instability. With a considerable level of two-dimensional disturbance, the vortex tube nonlinearly develops from the T-S-like wave, and then either deforms into a -vortex in the near-wall region or rolls up to the free shear region. The further burst of turbulence can follow the first pathway as K-type transition or the second one as vortex tube breakdown due to the elliptical instability. Additionally, non-modal growth can initiate the inception of streaky structures by favourable three-dimensional initial perturbations and/or forcing. The secondary instabilities responsible for the streak breakdown are classified as the varicose (symmetric) and sinuous (anti-symmetric) modes. Under a sufficiently high level of three-dimensional disturbance, the bypass transition is predominantly characterised by the formation of the sinuous mode and turbulent spots, which leads to the suppression of inflection point instability.

Original languageEnglish
Article numberA45
JournalJournal of Fluid Mechanics
Volume943
DOIs
Publication statusPublished - 25 Jul 2022

Keywords

  • boundary layer stability
  • transition to turbulence

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Gong, M., Xiong, C., Mao, X., Cheng, L., Wang, S. P., & Zhang, A. M. (2022). Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer. Journal of Fluid Mechanics, 943, Article A45. https://doi.org/10.1017/jfm.2022.446