Stability of a self-similar adverse pressure gradient turbulent boundary layer

M. P. Eisfelder, J. S. Müller, A. Sekimoto, A. J. Buchner, V. Kitsios, C. Atkinson, K. Oberleithner, J. Soria

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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 (δ2) 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 (δ1) 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 kxr and phase velocity ĉr increase monotonically for both β cases. Comparisons with a quasi-laminar analysis are also made.

Original languageEnglish
Title of host publicationProceedings of the 21st Australasian Fluid Mechanics Conference
EditorsTimothy C.W. Lau, Richard M. Kelso
PublisherAustralasian Fluid Mechanics Society
Number of pages4
ISBN (Electronic)9780646597843
Publication statusPublished - 2018
EventAustralasian Fluid Mechanics Conference 2018 - Adelaide Convention Centre, Adelaide, Australia
Duration: 10 Dec 201813 Dec 2018
Conference number: 21st (Proceedings)


ConferenceAustralasian Fluid Mechanics Conference 2018
Abbreviated titleAFMC 2018
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