## Abstract

Linear stability analysis (LSA) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) is explored in order to identify coherent structures. An eddy viscosity model (EV) is implemented via the Boussinesq hypothesis [8] to model the nonlinear coherent-turbulent interactions. Direct numerical simulations (DNS) by Kitsios et al. [3, 6] are used for the database of this study. A weak APG and strong APG (on the verge of separation) are studied with dimensionless streamwise pressure gradients (β) of 1 and 39 respectively. Their Reynolds numbers based on the momentum thickness (δ_{2}) within their respective regions of interest are 3, 100 − 3, 400 and 10, 000 − 12, 300. For the strong APG, the most unstable eigen-solution produces a wave resembling a Kelvin-Helmholtz (KH) instability located near the displacement thickness (δ_{1}) height. This position coincides with the inflection point (IP) in the mean flow profile. The IP satisfies Rayleigh’s and Fjortoft’s criterion for the existence of an inviscid instability [9]. Positive growth rate is seen for non-dimensional angular frequencies of 0.08 ≤ ω ≤ 0.51, with the maximum growth occurring at ω = 0.26. The weak APG also contains a KH like wave, however for all ω, the growth rates are negative. Spanwise wavenumber k_{xr} and phase velocity ĉ_{r} increase monotonically for both β cases. Comparisons with a quasi-laminar analysis are also made.

Original language | English |
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Title of host publication | Proceedings of the 21st Australasian Fluid Mechanics Conference |

Editors | Timothy C.W. Lau, Richard M. Kelso |

Publisher | Australasian Fluid Mechanics Society |

Number of pages | 4 |

ISBN (Electronic) | 9780646597843 |

Publication status | Published - 2018 |

Event | Australasian Fluid Mechanics Conference 2018 - Adelaide Convention Centre, Adelaide, Australia Duration: 10 Dec 2018 → 13 Dec 2018 Conference number: 21st http://www.afms.org.au/proceedings/21.html (Proceedings) https://aomevents.eventsair.com/QuickEventWebsitePortal/21st-australasian-fluid-mechanics-conference/afmc2018 |

### Conference

Conference | Australasian Fluid Mechanics Conference 2018 |
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Abbreviated title | AFMC 2018 |

Country/Territory | Australia |

City | Adelaide |

Period | 10/12/18 → 13/12/18 |

Internet address |