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Convective instability and transient growth in flow over a backward-facing step

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Blackburn, H. M., Barkley, Dwight and Sherwin, Spencer J.. (2008) Convective instability and transient growth in flow over a backward-facing step. Journal of Fluid Mechanics, Vol.603 . pp. 271-304. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112008001109

Abstract

Transient energy growths of two- and three-dimensional optimal linear perturbations to two-dimensional flow in a rectangular backward-facing-step geometry with expansion ratio two are presented. Reynolds numbers based on the step height and peak inflow speed are considered in the range 0–500, which is below the value for the onset of three-dimensional asymptotic instability. As is well known, the flow has a strong local convective instability, and the maximum linear transient energy growth values computed here are of order 80×103 at Re = 500. The critical Reynolds number below which there is no growth over any time interval is determined to be Re = 57.7 in the two-dimensional case. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. Sub-optimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal three-dimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than two-dimensional cases, they are broadly similar in character. When the inflow of the full nonlinear system is perturbed with white noise, narrowband random velocity perturbations are observed in the downstream channel at locations corresponding to maximum linear transient growth. The centre frequency of this response matches that computed from the streamwise wavelength and mean advection speed of the predicted optimal disturbance. Linkage between the response of the driven flow and the optimal disturbance is further demonstrated by a partition of response energy into velocity components.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Reynolds number, Stability, Perturbation (Mathematics), Unsteady flow (Fluid dynamics), Fluid dynamics
Journal or Publication Title:	Journal of Fluid Mechanics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date:	May 2008
Volume:	Vol.603
Page Range:	pp. 271-304
Identification Number:	10.1017/S0022112008001109
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Australian Partnership for Advanced Computing (APAC), Ville de Paris (VdP)
Grant number:	EP/E006493/1 (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/868