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Multimedia files – 8/13 Sinusoidal and varicose instabilities of streaks in a boundary layer Contents: 1. Instabilities of streaky structures 2. Test model 3. Velocity field downstream of the roughness element 4. Antisymmetric sinusoidal instability mode, u tot 5. Antisymmetric sinusoidal instability mode, u ave 6. Symmetric varicose instability mode, u tot 7. Symmetric varicose instability mode, u ave 8. Related publications

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Instantaneous velocities in x-z plane: sinous (odd) mode (top) and varicose (even) mode (bottom) (Li & Malik 1995) 1. Instabilities of streaky structures (I) (see page of notes)

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Numerical simulation of the sinusoidal instability of streaky structures in a turbulent boundary layer; x-z (top) and x-y (bottom) planes (Brandt 2002) Numerical simulation of the varicose instability of streaky structure (Skote et al. 2002) (see page of notes) 1. Instabilities of streaky structures (II)

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Excitation of a sinusoidal instability mode Excitation of a varicose instability mode Excitation of a streaky structure 2. Test model (see page of notes) Flat-plate model designed for examination of the streak instabilities

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Perturbed flow behind the roughness element at x – x 0 = 30 mm for the sinusoidal (a) and varicose (b) instabilities. Filled contours show rms amplitude of the secondary high-frequency disturbances u' as m/s. Lines depict contours of mean velocity at levels of 15, 30, 45, 60 and 75% of U (a)(a) (b)(b) 3. Velocity field downstream of the roughness element (see page of notes)

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Streak breakdown through the sinusoidal instability. Isosurfaces of total instantaneous flow perturbation u tot (yellow – positive, blue – negative) at different levels: ± 10.3 %, ± 6.4 %, ± 2.6 %, and ± 0.65 % of U, from left to right 4. Antisymmetric sinusoidal instability mode, u tot (I) (see page of notes)

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A video clip (hot-wire visualization) by Chernoray V.G., Kozlov V.V., Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004) 4. Antisymmetric sinusoidal instability mode, u tot (II) Click to play

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Spatial patterns of the development of high-frequency disturbance of the sinusoidal instability: contours of rms velocity amplitude at x – x 0 =114 mm (top); isosurfaces of time-periodic velocity u': ± 6.4 %, 2.6 %, 1.3 %, and 0.65 % of U, from left to right (bottom) 5. Antisymmetric sinusoidal instability mode, u ave (I) (see page of notes)

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5. Antisymmetric sinusoidal instability mode, u ave (II) A video clip (hot-wire visualization) by Chernoray V.G., Kozlov V.V., Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004) Click to play

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6. Symmetric varicose instability mode, u tot (I) Streak breakdown through the varicose instability. Isosurfaces of total instantaneous flow perturbation u tot (yellow – positive, blue – negative) at different levels: ± 10.3 %, 6.4 %, 2.6 %, and 0.65 % of U, from left to right (see page of notes)

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6. Symmetric varicose instability mode, u tot (II) A video clip (hot-wire visualization) by Chernoray V.G., Kozlov V.V., Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004) Click to play

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7. Symmetric varicose instability mode, u ave (I) Spatial patterns of the development of high-frequency disturbance of the varicose instability: contours of rms velocity amplitude at x – x 0 =114 mm (top); isosurfaces of time-periodic velocity : ± 2.6%, 1.3%, 0.65% and 0.4% of U, from left to right (bottom) (see page of notes)

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7. Symmetric varicose instability mode, u ave (II) A video clip (hot-wire visualization) by Chernoray V.G., Kozlov V.V., Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004) Click to play

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Adrian R.J., Meinhart C.D., Tomkins C.D. (2000) Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech., 422, Asai M., Minagawa M., Nishioka M. (2002) The stability and breakdown of near-wall low-speed streak. J. Fluid Mech., 455, Bippes H. (1972) Experimentelle Untersuchung des laminar-turbulenten Umschlags an einer parallel angestroemten konkaven Wand. Sitzungsberichte der Heidelberger Akademie der Wissenschaften Mathematisch-naturwissenschaftliche Klasse, Jahrgang, 3 Abhandlung, (also NASA-TM-72243, March 1978). Brandt L., Heningsson D.S. (2002) Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech., 472, Chernoray, V.G., Kozlov, V.V., Löfdahl, L., Chun, H.H. (2006) Visualization of sinusoidal and varicose instabilities of streaks in a boundary layer. J. Visualization, 9(4), Litvinenko Yu.A., Chernorai V.G., Kozlov V.V., Loefdahl L., Grek G.R., Chun H.H. (2004) Nonlinear sinusoidal and varicose instability in the boundary layer (Review). Thermophysics and Aeromechanics, 11(3), Litvinenko Yu.A., Chernorai V.G., Kozlov V.V., Loefdahl L., Grek G.R., Chun H.H. (2005) Nonlinear sinusoidal and varicose instability in the boundary layer. Doklady Physics, 50(3), 147–150. Haidary H.A., Smith C.R. (1994) The generation and regeneration of single hairpin vortices. J. Fluid Mech., 227, Hamilton H., Kim J., Waleffe F. (1995) Regeneration of near-wall turbulence structures. J. Fluid Mech., 287, Ito A. (1985) Breakdown structure of longitudinal vortices along a concave wall. J. Japan Soc. Aero. Space Sci., 33, Kawahara G., Jimenez J., Uhlmann M., Pinelli A. (1998) The instability of streaks in near-wall turbulence. Center for Turbulence Research, Annual Research Briefs, Related publications (I)

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8. Related publications (II) Konishi Y., Asai M. (2004) Experimental investigation of the instability of spanwise-periodic low-speed streaks in a laminar boundary layer. Japan Fluid Mech. J., , Panton R.L. (2001) Overview of the self-sustaining mechanisms of wall turbulence. Progr. Aerosp. Sci., 37, Robinson S.K. (1991) The kinematics of turbulent boundary layer structure. NASA TM Schoppa W., Hussain F. (1997) Genesis and dynamics of coherent structures in near-wall turbulence: A new look. Self-sustaining Mechanisms of Wall Turbulence, R.L. Panton (ed.), Computational mechanics, Southampton. Skote M., Haritonidis J.H., Henningson D.S. (2002) Varicose instabilities in turbulent boundary layers. Phys. Fluids, 4(7),

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