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Compressibility effects on the structural evolution of transitional high-speed planar wakes

Published online by Cambridge University Press:  28 April 2016

Jean-Pierre Hickey
Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada
Fazle Hussain
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Xiaohua Wu
Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada


The compressibility effects on the structural evolution of the transitional high-speed planar wake are studied. The relative Mach number ( $Ma_{r}$ ) of the laminar base flow modifies two fundamental features of planar wake transition: (i) the characteristic length scale defined by the most unstable linear mode; and (ii) the domain of influence of the structures within the staggered two-dimensional vortex array. Linear stability results reveal a reduced growth (approximately 30 % reduction up to $Ma_{r}=2.0$ ) and a quasilinear increase of the wavelength of the most unstable, two-dimensional instability mode (approximately 20 % longer over the same $Ma_{r}$ range) with increasing $Ma$ . The primary wavelength defines the length scale imposed on the emerging transitional structures; naturally, a longer wavelength results in rollers with a greater streamwise separation and hence also larger circulation. A reduction of the growth rate and an increase of the principal wavelength results in a greater ellipticity of the emerging rollers. Compressibility effects also modify the domain of influence of the transitional structures through an increased cross-wake and inhibited streamwise communication as characteristic paths between rollers are deflected due to local $Ma$  gradients. The reduced streamwise domain of influence impedes roller pairing and, for a sufficiently large relative $Ma$ , pairing is completely suppressed. Thus, we observe an increased two-dimensionality with increasing Mach number: directly contrasting the increasing three-dimensional effects in high-speed mixing layers. Temporally evolving direct numerical simulations conducted at $Ma=0.8$ and 2.0, for Reynolds numbers up to 3000, support the physical insight gained from linear stability and vortex dynamics studies.

© 2016 Cambridge University Press 

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