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

Carpenter, P. W., Kudar, K. I., Ali, R., Sen, P. K. and Davies, Christopher 2007. A deterministic model for the sublayer streaks in turbulent boundary layers for application to flow control. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365 (1859) , pp. 2419-2441. 10.1098/rsta.2007.2016

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: sublayer streaks; bursting cycle; turbulent boundary layers
Publisher: The Royal Society
ISSN: 1364-503X
Last Modified: 04 Jun 2017 03:41
URI: http://orca-mwe.cf.ac.uk/id/eprint/25013

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