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Scaling of square-prism shear layers

Published online by Cambridge University Press:  28 June 2018

D. C. Lander Open the ORCID record for D. C. Lander [Opens in a new window] ,
D. M. Moore ,
C. W. Letchford  and
M. Amitay
D. C. Lander*
Affiliation:
Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
D. M. Moore
Affiliation:
Center for Flow Physics and Control, Department of Mechanical, Nuclear and Aerospace Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
C. W. Letchford
Affiliation:
Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
M. Amitay
Affiliation:
Center for Flow Physics and Control, Department of Mechanical, Nuclear and Aerospace Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
*
†Email address for correspondence: landed2@rpi.edu
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Abstract

Scaling characteristics, essential to the mechanisms of transition in square-prism shear layers, were explored experimentally. In particular, the evolution of the dominant instability modes as a function of Reynolds number were reported in the range $1.5\times 10^{4}\lesssim Re_{D}\lesssim 7.5\times 10^{4}$. It was found that the ratio between the shear layer frequency and the shedding frequency obeys a power-law scaling relation. Adherence to the power-law relationship, which was derived from hot-wire measurements, has been supported by two additional and independent scaling considerations, namely, by particle image velocimetry measurements to observe the evolution of length and velocity scales in the shear layer during transition, and by comparison to direct numerical simulations to illuminate the properties of the front-face boundary layer. The nonlinear dependence of the shear layer instability frequency is sustained by the influence of $Re_{D}$ on the thickness of the laminar front-face boundary layer. In corroboration with the original scaling argument for the circular cylinder, the length scale of the shear layer was the only source of nonlinearity in the frequency ratio scaling, within the range of Reynolds numbers reported. The frequency ratio scaling may therefore be understood by the influence of $Re_{D}$ on the appropriate length scale of the shear layer. This length scale was observed to be the momentum thickness evaluated at a transition point, defined where the Kelvin–Helmholtz instability saturates.

JFM classification

Wakes/Jets: Shear layers Instability: Transition to turbulence Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 1096 - 1119
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Copyright
© 2018 Cambridge University Press 

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