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Acoustic forcing of oblique wave resonance in the far wake

Published online by Cambridge University Press:  26 April 2006

C. H. K. Williamson  and
A. Prasad
C. H. K. Williamson
Affiliation:
Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA
A. Prasad
Affiliation:
Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA
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Abstract

In this paper, we investigate to what extent the far-wake ‘signature’ of the near-wake vortex dynamics of a nominally two-dimensional bluff body is affected by the character of the free-stream noise. We confirm the existence of an oblique wave resonance (at frequency, fK–fT), which is caused by nonlinear ‘quadratic’ interactions between primary oblique shedding waves (fK) and secondary two-dimensional waves (fT), which are amplified from free-stream disturbances. In this work, oblique wave resonance is induced by acoustic forcing of two-dimensional waves. The use of acoustic forcing reveals a set of higher-order oblique wave resonances corresponding to frequencies (fK–nfT), where n is an integer. We find from visualization that, even when the secondary two-dimensional waves have the same frequency as the oblique waves, it is the oblique waves that are preferentially amplified. Oblique wave angles up to 74° have been observed. The response of the wake to a large range of forcing frequencies shows a broad region of peak response, centred around F = (fT/fK) = 0.55, and is in reasonable agreement with predictions from linear stability analysis. A similar broad response is found for each of the higher-order oblique wave modes. Simple equations for the oblique waves yield approximate conditions for maximum wake response, with a frequency for peak response given by Fmax = 1/2n = 1/2, 1/4, 1/6,…, and an oblique wave angle given by θmax = 2θK, where θK is the angle of oblique vortex shedding. An increase in forcing amplitude has the effect of bringing the nonlinear wave interactions, leading to oblique wave resonance, further upstream. Paradoxically, the effect of an increase in amplitude (A) of the two-dimensional wave forcing is to further amplify the oblique waves in preference to the two-dimensional waves and, under some conditions, to inhibit the appearance of prominent two-dimensional waves where they would otherwise appear. With a variation in forcing amplitude, the amplitude of oblique wave response is found to be closely proportional to A½. In summary, this investigation confirms the surprising result that it is only through the existence of noise in the free stream that the far wake is ‘connected’ to the near wake.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 315 - 341
Copyright
© 1993 Cambridge University Press

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