Streak breakdown in bypass transitionDan Henningson
Department of Mechanics, KTH
Collaborators:
Philipp Schlatter, KTH
Luca Brandt, KTH
Rick de Lange, TU/e
Streak breakdown in bypass transition
Dan Henningson
Department of Mechanics, KTH
Collaborators:
Philipp Schlatter, KTH
Luca Brandt, KTH
Rick de Lange, TU/e
Bypass transition
Freestream turbulence induces streaks, which break down to turbulent spots due to secondary instability
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
Streak breakdown
Brandt, Schlatter & Henningson 2004 Mans, de Lange & van Steenhoven 2007 Eindhoven experiments and KTH simulations show both sinuous and varicose breakdown
Is this secondary instability of streaks?
A x A0 Optimal perturbations used as inflow conditions with different initial amplitudes A0 in DNS Brandt & Henningson 2002
Impulse response using DNS on frozen streak
x z Fundamental modes: A=0.36, X=630. Brandt, Cossu, Chomaz, Huerre & Henningson 2003
Streak impulse response
Temporal growth rate s 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 s v Re s a A Brandt, Cossu, Chomaz, Huerre & Henningson 2003
Secondary instability structures
Non-linear development of impulse response on spatially evolving streak
Vortex structures at breakdown similar to breakdown under FST
Secondary instability structures
Non-linear development of impulse response on spatially evolving streak
Vortex structures at breakdown similar to breakdown under FST
Comparison of impulse and bypass structure
Oscillations of low speed streaks in non-linear impulse strikingly similar to spot precursors in bypass transition
Streak breakdown caused by secondary instability
Zaki & Durbin model
Zaki & Durbin 2005 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%
Breakdown in model simulation
3D structures show subharmonic sinuous breakdown
Vortical structures above oscillating low-speed streak
2D cut of breakdown in model
2D cut resembles Kelvin-Helmholtz instability
Claimed by Durbin & Wu to be responsible for breakdown in recent Annu. Rev. Fluid Mech.
Sinuous oscillations claimed to be artifact of plotting
Comparison of secondary instability characteristics
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
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