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Three-dimensional instability in flow over a backward-facing step. (English) Zbl 1026.76019
Summary: 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 number 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.

76E15 Absolute and convective instability and stability in hydrodynamic stability
76M22 Spectral methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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