A deterministic model for the sublayer streaks in turbulent boundary layers for application to flow control

Peter W. Carpenter, Karen L. Kudar, Reza Ali, Pradeep K. Sen, Christopher Davies

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)

    Abstract

    We present a relatively simple, deterministic, theoretical model for the sublayer streaks in a turbulent boundary layer based on an analogy with Klebanoff modes. Our approach is to generate the streamwise vortices found in the buffer layer by means of a vorticity source in the form of a fictitious body force. It is found that the strongest streaks correspond to a spanwise wavelength that lies within the range of the experimentally observed values for the statistical mean streak spacing. We also present results showing the effect of streamwise pressure gradient, Reynolds number and wall compliance on the sublayer streaks. The theoretical predictions for the effects of wall compliance on the streak characteristics agree well with experimental data. Our proposed theoretical model for the quasi-periodic bursting cycle is also described, which places the streak modelling in context. The proposed bursting process is as follows: (i) streamwise vortices generate sublayer streaks and other vortical elements generate propagating plane waves, (ii) when the streaks reach a sufficient amplitude, they interact nonlinearly with the plane waves to produce oblique waves that exhibit transient growth, and (iii) the oblique waves interact nonlinearly with the plane wave to generate streamwise vortices; these in turn generate the sublayer streaks and so the cycle is renewed.

    Original languageEnglish
    Pages (from-to)2419-2441
    Number of pages23
    JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Volume365
    Issue number1859
    DOIs
    Publication statusPublished - 15 Oct 2007

    Keywords

    • Bursting cycle
    • Sublayer streaks
    • Turbulent boundary layers

    ASJC Scopus subject areas

    • Mathematics(all)
    • Engineering(all)
    • Physics and Astronomy(all)

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