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

Thomas, Christian, Hall, Philip and Davies, Christopher 2015. Nonlinear effects on the receptivity of cross-flow in the swept Hiemenz flow. Journal of Fluid Mechanics 763 , pp. 433-459. 10.1017/jfm.2014.688

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Boundary layer receptivity; Boundary layer stability; Nonlinear instability
Additional Information: Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0022-1120/ (accessed 16/03/2015)
Publisher: Cambridge University Press (CUP)
ISSN: 0022-1120
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 24 November 2014
Last Modified: 25 Feb 2020 22:39
URI: http://orca-mwe.cf.ac.uk/id/eprint/67890

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