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

By Hugh Maurice Blackburn, Dwight Barkley, Spencer J. Sherwin. Journal of Fluid Mechanics, 2007

201 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/622c99a975a270dd60a62d95d90b6637201cb606

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Global and Planetary Change

Citations in the corpus

Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers (2010, methodology): “This has not been done previously for Optimal disturbances in the Blasius boundary-layer flow 197 the Blasius flow, although Blackburn et al. (2008) computed several optimals for the flow past a backward-facing step.”
Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach (2010, background): “[145,146] on a backward facing step and stenotic flows.”
Direct optimal growth analysis for timesteppers (2008, background): “Backward-facing step Our first example of transient growth analysis concerns steady flow over a backward-facing step [10], which is almost infamous as having localized convective instability.”
Stability and transition of three-dimensional boundary layers (2013, methodology): “(1993), Reddy & Henningson (1993), and Blackburn et al. (2008)).”
Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer (2013, background): “For open flows, most of the theoretical studies [10–13] have been performed in the temporal domain.”
Input–output analysis, model reduction and control of the flat-plate boundary layer (2009, methodology): “The timestepper technique has become increasingly popular in stability analysis, for both computing the largest transient growth ( Blackburn, Barkley & Sherwin 2008 ) and performing asymptotic analysis (Barkley, Gomes & Henderson 2002).”