Journal of Fluid Mechanics



Three-dimensional instability in flow over a backward-facing step


DWIGHT BARKLEY a1, M. GABRIELA M. GOMES a1 and RONALD D. HENDERSON a2
a1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
a2 Aeronautics and Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

(Received April 10 2002)
(Revised July 1 2002)



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