1. 1 Linné Flow Centre KTH Mechanics Streak breakdown in bypass transition Dan Henningson Department of Mechanics, KTH Collaborators: Philipp Schlatter, KTH Luca Brandt, KTH Rick de Lange, TU/e

2. 2 Linné Flow Centre KTH Mechanics Bypass transition Freestream turbulence induces streaks, which break down to turbulent spots due to secondary instability

3. 3 Linné Flow Centre KTH Mechanics Bypass Transition moderate to high levels of free-stream turbulence Non-modal growth of streaks Secondary instability of streaks Turbulent spots Turbulence Jacobs & Durbin 2000 Simulations of bypass transition, J. Fluid Mech. 428, 185-212. Matsubara & Alfredsson 2001 Disturbance growth in boundary layers subject to free-stream turbulence, J. Fluid Mech. 430, 149-168. Brandt, Schlatter & Henningson 2004 Transition in boundary layers subject to free-stream turbulence, J. Fluid Mech. 517, 167-198. Durbin & Wu 2007 Transition beneath vortical disturbances, Ann. Rev. Fluid Mech. 39, 107-128. Mans, de Lange & van Steenhoven 2007 Sinuous breakdown in a flat plate boundary layer exposed to free-stream turbulence, Phys. Fluids 19, 088101. Matsubara & Alfredsson 2001

4. 4 Linné Flow Centre KTH Mechanics Streak breakdown Eindhoven experiments and KTH simulations show both sinuous and varicose breakdown Is this secondary instability of streaks? Brandt, Schlatter & Henningson 2004Mans, de Lange & van Steenhoven 2007

5. 5 Linné Flow Centre KTH Mechanics Non-modal growth of 3D streaks Optimize streak output E out / vortex input E in Andersson, Berggren & Henningson 1999

6. 6 Linné Flow Centre KTH Mechanics Nonlinear saturated streaks A x A0A0 Optimal perturbations used as inflow conditions with different initial amplitudes A 0 in DNS Brandt & Henningson 2002

7. 7 Linné Flow Centre KTH Mechanics Impulse response using DNS on frozen streak x z Fundamental modes: A=0.36, X=630. Brandt, Cossu, Chomaz, Huerre & Henningson 2003

8. 8 Linné Flow Centre KTH Mechanics Streak impulse response Temporal growth rate  traveling at velocity v Streak instability is convective! Group velocity ≈ 0.8 Growth rate approaches invicid limit as Re increases A= 0.28, 0.31, 0.34, 0.36, 0.38  v Re   A Brandt, Cossu, Chomaz, Huerre & Henningson 2003

9. 9 Linné Flow Centre KTH Mechanics Secondary instability structures Non-linear development of impulse response on spatially evolving streak Vortex structures at breakdown similar to breakdown under FST

10. 10 Linné Flow Centre KTH Mechanics Secondary instability structures Non-linear development of impulse response on spatially evolving streak Vortex structures at breakdown similar to breakdown under FST

11. 11 Linné Flow Centre KTH Mechanics Zaki & Durbin model Simple model of bypass transition starting with interacting continuous spectrum modes Low-frequency penetrating mode & high-freq. non-penetrating mode (streak + secondary instability) Initial conditions with vrms 2% Zaki & Durbin 2005

12. 12 Linné Flow Centre KTH Mechanics Breakdown in model simulation 3D structures show subharmonic sinuous breakdown Vortical structures above oscillating low-speed streak

13. 13 Linné Flow Centre KTH Mechanics 2D cut of breakdown in model 2D cut resembles Kelvin-Helmholtz instability Erroneously claimed by Durbin & Wu to be responsible for breakdown in recent Annu. Rev. Fluid Mech. Sinuous oscillations claimed to be artifact of plotting

14. 14 Linné Flow Centre KTH Mechanics Comparison of secondary instability characteristics Sinuous instability WavelengthGrowthratePropagation velocity Visualization Inviscid instability 10.40.035 Linear impulse response 10.40.0320.65 – 0.8 – 0.95 Non-linear impulse 110.0250.55 – 0.8 – 0.95 Zaki-Durbin model 200.85 KTH simulations 7 - 110.85 TU/e experiments 9 - 160.010.8

15. 15 Linné Flow Centre KTH Mechanics Conclusions Sinuous breakdown in bypass transition is caused by secondary instability of streaks Characteristics of breakdown similar in experiments and simulations of full bypass transition, impulse response and Zaki & Durbin model 2D cuts of 3D simulations have mistakenly been interpreted as evidence of Kelvin-Helmholtz instability Varicose breakdown needs additional investigations. However, sinuous is more common