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, utot
5. Antisymmetric sinusoidal instability mode, uave
6. Symmetric varicose instability mode, utot
7. Symmetric varicose instability mode, uave
8. Related publications
1. Instabilities of streaky structures (I)
Instantaneous velocities in x-z plane: sinous (odd) mode (top)
and varicose (even) mode (bottom) (Li & Malik 1995)
(see page of notes)
1. Instabilities of streaky structures (II)
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)
2. Test model
Excitation of a varicose instability mode
Excitation of a streaky structure
Excitation of a sinusoidal instability mode
Flat-plate model designed for examination of the streak instabilities
(see page of notes)
3. Velocity field downstream of the roughness element
(a)
(b)
Perturbed flow behind the roughness element at x – x0 = 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
(see page of notes)
4. Antisymmetric sinusoidal instability mode, utot (I)
Streak breakdown through the sinusoidal instability. Isosurfaces of total instantaneous
flow perturbation utot (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)
4. Antisymmetric sinusoidal instability mode, utot (II)
Click to play
A video clip (hot-wire “visualization”) by Chernoray V.G., Kozlov V.V.,
Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004)
5. Antisymmetric sinusoidal instability mode, uave (I)
Spatial patterns of the development of high-frequency disturbance of the sinusoidal
instability: contours of rms velocity amplitude at x – x0 =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)
(see page of notes)
5. Antisymmetric sinusoidal instability mode, uave (II)
Click to play
A video clip (hot-wire “visualization”) by Chernoray V.G., Kozlov V.V.,
Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004)
6. Symmetric varicose instability mode, utot (I)
Streak breakdown through the varicose instability. Isosurfaces of total instantaneous
flow perturbation utot (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)
6. Symmetric varicose instability mode, utot (II)
Click to play
A video clip (hot-wire “visualization”) by Chernoray V.G., Kozlov V.V.,
Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004)
7. Symmetric varicose instability mode, uave (I)
Spatial patterns of the development of high-frequency disturbance of the varicose
instability: contours of rms velocity amplitude at x – x0 =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)
7. Symmetric varicose instability mode, uave (II)
Click to play
A video clip (hot-wire “visualization”) by Chernoray V.G., Kozlov V.V.,
Löfdahl L., Litvinenko Yu.A., Grek G.R., Chun H. (2004)
(see page of notes)
8. Related publications (I)
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, 1-23.
Asai M., Minagawa M., Nishioka M. (2002) The stability and breakdown of near-wall low-speed streak.
J. Fluid Mech., 455, 289-314.
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, 103-180. (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, 229-261.
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), 437-444.
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), 329-353.
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, 135-151.
Hamilton H., Kim J., Waleffe F. (1995) Regeneration of near-wall turbulence structures. J. Fluid Mech.,
287, 317-348.
Ito A. (1985) Breakdown structure of longitudinal vortices along a concave wall. J. Japan Soc. Aero. Space Sci.,
33, 166-173.
Kawahara G., Jimenez J., Uhlmann M., Pinelli A. (1998) The instability of streaks in near-wall turbulence.
Center for Turbulence Research, Annual Research Briefs, 155-170.
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., 021257, 55-67.
Panton R.L. (2001) Overview of the self-sustaining mechanisms of wall turbulence. Progr. Aerosp. Sci.,
37, 341-383.
Robinson S.K. (1991) The kinematics of turbulent boundary layer structure. NASA TM 103859.
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), 2309-2323.