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Boundary-layer pressures and the Corcos model: a development to incorporate low-wavenumber constraints

Published online by Cambridge University Press:  20 April 2006

J. E. Ffowcs Williams
J. E. Ffowcs Williams
Affiliation:
Department of Engineering, University of Cambridge
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Abstract

This paper re-examines the theoretical arguments that indicate the structure of the pressure field induced on a flat surface by boundary-layer turbulence at low Mach number. The long-wave elements are shown to be dictated by the acoustics of the flow, and the limit of the acoustic range is the coincidence condition of grazing waves where the spectrum is singular and proportional to the logarithm of the flow scale. The surface spectrum is shown to be proportional to the square of frequency at low-enough frequency and to the square of wavenumber at those low wavenumbers with subsonic phase speed.

The similarity model successfully used by Corcos for the main convective elements of the field is used in this paper to model the turbulent sources of pressure, not the pressure itself, so that a Corcos-like description of the pressure spectrum is derived that is consistent with constraints imposed by the governing equations. This results in a fairly compact specification of the pressure spectrum with yet-undetermined constants, which must be derived from experiment. Despite an extensive search of published data on the pressure field, it is concluded that existing information is an inadequate basis for setting those constants and that new free field experiments are needed. Boundary layers formed on gliders or buoyant underwater bodies offer the most promising source of such data.

The paper concludes with a study of how large flush-mounted transducers discriminate against the local flow noise field and i t is shown that they do so at a rate of 9 decibels per doubling of transducer diameter. This different conclusion from Corcos’ correct 6 decibel rate for small transducers is entirely due to the low- wavenumber constraints on the spectrum, which are misrepresented in the simple similarity model. This result, which conforms with the constraints imposed by the weak compressibility of the fluid, is the same as that later suggested by Corcos for transducers that are large on the boundary-layer scale.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 9 - 25
Copyright
© 1982 Cambridge University Press

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