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Instability mode interactions in a spatially developing plane wake

Published online by Cambridge University Press:  26 April 2006

Hiroshi Maekawa ,
Nagi N. Mansour  and
Jeffrey C. Buell
Hiroshi Maekawa
Affiliation:
Department of Mechanical Engineering, Kagoshima University, Kagoshima 890, Japan Present address: Department of Mechanical and Control Engineering, University of Electro-Communications, Chofu, Tokyo I82, Japan.
Nagi N. Mansour
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Jeffrey C. Buell
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

The transition mechanism in a spatially developing two-dimensional wake is studied by means of direct numerical simulations. Five different types of forcing of the inlet are investigated: fundamental mode, fundamental and one or two subharmonics, fundamental mode and random noise, and random noise only. The effects of the amplitude levels of the perturbations on the development of the layer are also investigated. Statistical analyses are performed and some numerical results are compared with experimental measurements. When only a fundamental mode is forced, the energy spectra show amplification of the fundamental frequency and its higher harmonics, and the development of a stable vortex street. When the inlet flow is forced by a fundamental mode and two subharmonics, a vortex street also appears downstream, but the shape of the vortices is distorted. The amplitude of the subharmonic grows only after the saturation of the fundamental. Amplification of modes close to the fundamental mode is observed when random noise of large amplitude is added to the fundamental mode. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the flow structure are observed. Pairing of vortices of the same sign is observed, as well as coupling of vortices of opposite sign. When the inlet profile is forced by random noise of amplitude 10−5 times the free-stream velocity, one frequency close to the most unstable one is amplified more than the others. The energy spectrum is otherwise full. When the same low amplitude (10−5) is used to force the fundamental mode and its two subharmonics, bands of energy develop around the forced modes and their harmonics. Finally, we find that large-deficit wakes are globally unstable when the size of the absolutely unstable region is greater than about three times the half-width of the wake

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 235 , February 1992 , pp. 223 - 254
Copyright
© 1992 Cambridge University Press

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