Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer

By C. Cossu, Luca Brandt. 2002

206 citations recorded by the source corpus.

In this Letter we show by numerical simulation that streamwise streaks of sufficiently large amplitude are able to stabilize Tollmien–Schlichting waves in zero pressure gradient boundary layers at least up to Re=1000. This stabilization is due to the spanwise averaged part of the nonlinear basic flow distortion induced by the streaks and occurs for streak amplitudes lower than the critical threshold beyond which secondary inflectional instability is observed. A new control strategy is implemented using optimal perturbations in order to generate the streaks.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/14d608f69eaf2795517ec3fd6361df49e395c228

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In Computational Mechanics

Citations in the corpus

On Tollmien–Schlichting-like waves in streaky boundary layers (2004, methodology): “The analysis of the growth rates of the streaky-TS waves confirms the stabilising effect of steady streaks on the viscous instability [18,41] and that this stabilising effect increases with the streak amplitude.”
Optimal transient growth and very large–scale structures in turbulent boundary layers (2008, methodology): “Such a paradigm has been successfully applied to stabilize Tollmien–Schlichting waves in a laminar boundary layer (Cossu & Brandt 2002; Fransson et al. 2005) and effectively delay the transition to turbulence (Fransson et al. 2006).”
Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks (2011, background): “Both a stabilizing and a destabilizing influence have been suggested in the literature (e.g. Cossu & Brandt 2002; Liu, Zaki & Durbin 2008b).”
Transition in boundary layers subject to free-stream turbulence (2004, result): “These authors observed that the linear amplification rate of the Tollmien–Schlichting waves evolving under free-stream turbulence is lower than in the undisturbed Blasius boundary layer; a result later confirmed for steady streaks by the simulations in Cossu & Brandt (2002).”
Direct numerical simulations of transition in a compressor cascade: the influence of free-stream turbulence (2010, methodology): “S waves – a view supported by analyses (Cossu & Brandt 2002) and experimental observations (Fransson et al. 2005).”
Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number (2010, methodology): “This kind of approach has already proven successful in the laminar boundary layer where optimal laminar streaks have been used to stabilize Tollmien–Schlichting waves and delay transition (Cossu & Brandt 2002; Fransson et al. 2006).”
Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow (2010, background): “…amplifications, with amplitudes up to ≈13 % of Ue, and the leading-order effect on the base flow is instrumental in improving its stability with respect to Tollmien– Schlichting waves (Cossu & Brandt 2002, 2004; Fransson et al. 2005) and in delaying transition to turbulence (Fransson et al. 2006).”