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On the Generation of Instability Tollmien-Schlichting Waves by Free-Stream Turbulence

Part of: Incompressible viscous fluids Turbulence

Published online by Cambridge University Press:  09 January 2017

Luyu Shen  and
Changgen Lu
Luyu Shen*
Affiliation:
School of Marine Sciences, Nanjing University of Information Science & Technology, Nanjing 210044, China
Changgen Lu*
Affiliation:
School of Marine Sciences, Nanjing University of Information Science & Technology, Nanjing 210044, China
*
*Corresponding author. Email:shenluyu99@foxmail.com (L. Y. Shen), cglu@nuist.edu.cn (C. G. Lu)
*Corresponding author. Email:shenluyu99@foxmail.com (L. Y. Shen), cglu@nuist.edu.cn (C. G. Lu)
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Abstract

The beginning of the transition from the laminar to a turbulent flow is usually the generation of instability Tollmien-Schlichting (T-S) waves in the boundary layer. Previously, most numerical and experimental researches focused on generating instability T-S waves through the external disturbances such as acoustic waves and vortical disturbances interacting with wall roughness or at the leading-edge of flatplate, whereas only a few paid attention to the excitation of the T-S waves directly by free-stream turbulence (FST). In this study, the generating mechanism of the temporal mode T-S waves under free-stream turbulence is investigated by using direct numerical simulation (DNS) and fast Fourier transform. Wave packets superposed by a group of stability, neutral and instability T-S waves are discovered in the boundary layer. In addition, the relation between the amplitude of the imposed free-stream turbulence and the amplitude of the excited T-S wave is also obtained.

Keywords

Free-stream turbulenceTollmien-Schlichting waveboundary layer

MSC classification

Secondary: 76F65: Direct numerical and large eddy simulation of turbulence 76F40: Turbulent boundary layers 76D33: Waves
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 429 - 438
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Schubauer, G. B. and Skramstad, H. K., Laminar-boundary-layer oscillations and transition on a flat plate, Technical Report Archive & Image Library, 1948.Google Scholar
[2] Gaster, M., On the generation of spatially growing waves in a boundary layer, J. Fluid. Mech., 22 (1965), pp. 433–441.CrossRefGoogle Scholar
[3] Goldstein, M. E., The evolution of Tollmien-Sclichting waves near a leading edge, J. Fluid. Mech., 127 (1983), pp. 59–81.CrossRefGoogle Scholar
[4] Ruban, A. I., On the generation of Tollmien-Schlichting waves by sound, Fluid. Dynam., 19 (1984), pp. 709–717.Google Scholar
[5] Goldstein, M. E., Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry, J. Fluid. Mech., 154 (1985), pp. 509–529.Google Scholar
[6] Duck, P. W., Ruban, A. I. and Zhikharev, C. N., The generation of Tollmien-Schlichting waves by free-stream turbulence, J. Fluid. Mech., 312 (1996), pp. 341–371.CrossRefGoogle Scholar
[7] Wu, X., On local boundary-layer receptivity to vortical disturbances in the free stream, J. Fluid. Mech., 449 (2001), pp. 373–393.CrossRefGoogle Scholar
[8] Lu, C. G. and Shen, L. Y., Numerical study on boundary-layer receptivity with localized wall blowing/suction, Acta Phys. Sin., 64 (2015), pp. 224702 (in Chinese).Google Scholar
[9] Shen, L. Y. and Lu, C. G., Boundary-layer receptivity under the interaction of free-stream turbulence and localized wall roughness, Appl. Math. Mech., 37 (2016), pp. 349–360.Google Scholar
[10] Shen, L. Y. and Lu, C. G., Local receptivity in the non-parallel boundary layer, Appl. Math. Mech., 37 (2016), pp. 929–940.CrossRefGoogle Scholar
[11] Wiegel, M. and Wlezien, R. W., Acoustic receptivity of laminar boundary layers over wavy walls, AIAA. P., (1993), 93–3280.Google Scholar
[12] Dietz, A. J., Local boundary-layer receptivity to a convected free-stream disturbance, J. Fluid. Mech., 378 (1999), pp. 291–317.Google Scholar
[13] Luo, J. S. and Zhou, H., On the generation of Tollmien-Schlichting waves in the boundary layer of a flat plate by the disturbances in the free stream, P. Roy. Soc. A-Math. Phy., 413 (1987), pp. 351–367.Google Scholar
[14] Wu, X., Generation of Tollmien-Schlichting waves by convecting gusts interacting with sound, J. Fluid. Mech., 397 (1999), pp. 285–316.CrossRefGoogle Scholar
[15] Zhang, Y., Zaki, T. and Sherwin, S. et al., Nonlinear response of a laminar boundary layer to isotropic and spanwise localized free-stream turbulence, 6th AIAA. Theory Fluid. Mech. Con., 2011.CrossRefGoogle Scholar
[16] Shen, L. Y., Lu, C. G., and Wu, W. G. et al., A high-order numerical method to study three-dimensional hydrodynamics in a natural river, Adv. Appl. Math. Mech., 7 (2015), pp. 180–195.Google Scholar
[17] Lu, C., Cao, W. and Zhang, Y. et al., Large eddies induced by local impulse at wall of boundary layer with pressure gradients, Prog. Nat. Sci., 18 (2008), pp. 873–878.Google Scholar
[18] Dietz, A. J., Boundary-layer receptivity to transient convected disturbances, AIAA. J., 36 (1998), pp. 1171–1177.Google Scholar