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Convective instability and transient growth in flow over a backwardfacing step
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Blackburn, H. M., Barkley, Dwight and Sherwin, Spencer J.. (2008) Convective instability and transient growth in flow over a backwardfacing step. Journal of Fluid Mechanics, Vol.603 . pp. 271304. ISSN 00221120

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Official URL: http://dx.doi.org/10.1017/S0022112008001109
Abstract
Transient energy growths of two and threedimensional optimal linear perturbations to twodimensional flow in a rectangular backwardfacingstep 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 threedimensional 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 twodimensional 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. Suboptimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal threedimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than twodimensional 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:  00221120 
Official Date:  May 2008 
Volume:  Vol.603 
Page Range:  pp. 271304 
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) 
References:  Barkley, D. 2005 Confined threedimensional stability analysis of the cylinder wake. Phys. Rev. E 71, 017301. 
URI:  http://wrap.warwick.ac.uk/id/eprint/868 
Data sourced from Thomson Reuters' Web of Knowledge
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