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Nonlinear effects on the receptivity of cross-flow in the swept Hiemenz flow

Published online by Cambridge University Press:  18 December 2014

Christian Thomas ,
Philip Hall  and
Christopher Davies
Christian Thomas*
Affiliation:
Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
Philip Hall
Affiliation:
Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
Christopher Davies
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
*
†Email address for correspondence: c.thomas@imperial.ac.uk
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Abstract

Nonlinear effects on the receptivity of cross-flow in the swept Hiemenz boundary layer are investigated. Numerical simulations are generated using a vorticity form of the Navier–Stokes equations. Steady perturbations are established using surface suction and blowing distributed along the spanwise direction as either a periodic strip or a band of small holes. The method of excitation, the size and the location of the prescribed forcing are shown to have a significant influence on the receptivity of the boundary layer. Blowing holes are found to excite perturbations with considerably larger magnitudes than those generated using a periodic suction and blowing strip. A semi-logarithmic relationship is derived that relates the initial amplitude of the linear-only disturbances with the location at which the absolute magnitude of the chordwise primary Fourier harmonic attains a stationary point or a size of approximately one-tenth of the free-stream spanwise velocity. Furthermore, the size of the physical chordwise velocity perturbation about this position can be estimated directly from the linear-only solutions. This would suggest that, for sufficiently small initial amplitudes, the onset of some nonlinear flow development properties can be predicted directly from a linear receptivity analysis.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability Instability: Nonlinear instability

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 433 - 459
Copyright
© 2014 Cambridge University Press 

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