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Resonant growth of three-dimensional modes in trnsitioning Blasius boundary layers

Published online by Cambridge University Press:  26 April 2006

T. C. Corke  and
R. A. Mangano
T. C. Corke
Affiliation:
Illinois Institute of Technology, Fluid Dynamics Research Center, Mechanical and Aerospace Engineering Department, Chicago, IL 60616, USA
R. A. Mangano
Affiliation:
Illinois Institute of Technology, Fluid Dynamics Research Center, Mechanical and Aerospace Engineering Department, Chicago, IL 60616, USA
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Abstract

By carefully controlled phase-coupled input of simultaneous two- and three-dimensional disturbances, the nonlinear evolution and breakdown of the laminar flow in a boundary layer was examined. This involved the generation of plane Tollmien–Schlichting waves and pairs of oblique waves so as to promote nearresonance conditions which have been theoretically shown to lead to the rapid development of three-dimensionality in unstble boundary layers. Special emphasis is placed on the two prominent mechanisms, namely resonant-triads of Orr–Sommerfeld modes and the secondary instability of the streamwise periodic flow to spanwise periodic three-dimensional disturbances. The sensitivity of these mechanisms on the amplitudes and wavenumbers of the input disturbances was of special focus.

The simultaneous two- and three-dimensional wave generation was accomplished using a spanwise array of line heaters suspended just above the wall at the approximate height of the critical layer in the laminar boundary layer. These were operated to produce, through local heating, time-periodic spanwise-phase-varying velocity perturbations. Of primary emphasis in this paper are conditions obtained by the combined forcing of fundamental plane waves with wavenumbers (α, 0) and pairs of subharmonic oblique waves (½α, ± β). The reslults document resonant growth of energy in the subharmonic modes, the formation of staggered lambda vortex patterns with a cross-stream scale commensurate with the seeded ± β condition, and their subsequet transition to turbulence. Complete documentation of the flow field at these various stages is presented using smoke-wire flow visualization and through phase-conditioned hot-wire surveys measuring all three velocity components in three space dimensions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 93 - 150
Copyright
© 1989 Cambridge University Press

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References

Bar-Sever, A. 1984 Boundary layer transition over rough surfaces. M.S. thesis, Illinois Institute of Technology.
Benney, D. J. 1964 Finite amplitude effects in an unstable laminar boundary, layer. Phys. Fluids 7, 319.Google Scholar
Benney, D. J. & Lin, C. C. 1960 On the secondary motion induced by oscillations in a shear flow. Phys. Fluids 3, 656.Google Scholar
Bertolotti, F. 1985 Temporal and spatial growth of subharmonic disturbances in Falkner—Sken flows. M.S. thesis, Virginia Polytechnic Institute State University.
Corke, T., Bar-Sever, A. & Morkovin, M. 1986 Experiments on transition enhancement by distributed roughness. Phys. Fluids 29, 3199.Google Scholar
Corke, T. & Dal-Ferro, P. 1987 Later stages of transition in three-dimensional seeded boundary layers. IIT Fluid Dynamics Center Rep. 87-2. (In preparation for J. Fluid Mech.)Google Scholar
Corke, T., Koga, D., Drubka, R. & Nagib, H. 1977 A new technique for introducing controlled sheets of smoke streaklines in wind tunnels. IEEE Publication 77-CH 1251-8 AES.Google Scholar
Corker, T. & Mangano, R. 1987 Transition of a boundary layer: controlled fundamental—subharmonic interactions. In Turbulent Management and Relaminarization, IUTAM Symp. Bangalore, India, pp. 199–213. Springer.
Corke, T. C., Shakib, F. & Nagib, H. M. 1985 Effects of low amplitude forcing on axisymmetic jet flows. AIAA Shear Flow Control Conf., Boulder, Colorado, AIAA-85-0573.Google Scholar
Corke, T. C., Shakib, F. & Nagib, H. M. 1989 Mode selection and resonant phase locking in unstable axisymmetric jets. J. Fluid Mech. (submitted).Google Scholar
Craik, A. D. D. 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393.Google Scholar
Crouch, J. D. 1988 The nonlinear evolution of secondary instabilities in boundary layers. Ph.D. thesis, Virginia Polytechnic Institute State University.
Dal-Ferro, P. 1987 Later stages of transition in three dimensional seeded boundary layers. M.S. thesis, Illinois Institute of Technology.
Hama, F. R. 1960 Boundary-layer transition induced by a vibrating ribbon on a flat plate. In Proc. 1960 Heat Transfer and Fluid Mechanics Institute, p. 92. Standford University Press.
Hasselman, K., Munk, W. & McDonald 1963 Bispectrum of ocean waves. In Proc. Symp. on Time Series Analysis (ed. M. Rosenblatt), pp. 125–139. Wiley.
Hhrbert, Th. 1983a Secondary instability of plane channel flow. Phys. Fluids 26, 871.Google Scholar
Herbert, Th. 1983b Subharmonic three-dimensional disturbances in unstable plane shear flows. AIAA paper 83–1759.Google Scholar
Herbert, Th. 1988 Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20, 487.Google Scholar
Herbert, Th. & Bertolotti, F. 1985 The effect of pressure gradients on the growth of subharmonic disturbances in boundary layers. In Proc. Conf. Low Reynolds Number Airfoil Aerodyn. (ed. T. Mueller), pp. 65–76. Note Dame University.
Herbert, Th. & Morkovin, M. V. 1980 Dialogue on bridging some gaps in stability and transition research. In Laminar—Turbulent Transition (ed. R. Eppler and H. Fasel), p. 47. Springer.
Hinich, M. J. & Clay, C. S. 1968 The application of the discrete Fourier transform in the estimation of power spectra, coherence and bispectra of geophysical data. Rev. Geophys 6, 347.Google Scholar
Kachanov, Yu. S. Koslov, V. V. & Levchenko, V. Ya. 1977 Nonlinear development of a wave in a boundary layer. Fluid Dyn. 12, 383.Google Scholar
Kachanov, Yu. S. & Levchenko, V. Ya. 1984 The resonant interacion of disturbances at laminar—turbulent transition in a boundary layer. J. Fluid Mech. 138, 209.Google Scholar
Kelly, R. E. 1968 On the resonant interaction of neutral disturbances in inviscid shear flows. J. Fluid Mech. 31, 789.Google Scholar
Klebanoff, P. S. & Tidstrom, K. D. 1959 Evolution of amplified waves leading to transition in a boundary layer with zero pressure gradient. NASA Tech. Note D195.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1.Google Scholar
Knisely, C. & Rockwel, D. 1981 Self-sustained low-frequency components in an impinging shear layer. J. Fluid Mech. 116, 157.Google Scholar
Liepmann, H. W., Brown, G. L. & Nosenchuck, D. M. Control of laminar-instability waves using a new technique. J. Fluid Mech. 118, 187.
Lii, K. S., Rosenblatt, M. & Van Atta, C. 1976 Bispectral measurements in turbulence. J. Fluid Mech. 77, 45–62.Google Scholar
Mangano, R. 1987 Transition of a boundary layer: controlled fundamental—subharmonic interactions. M.S. thesis, Illinois Institute of Technology.
Miksad, R., Jones, F. & Powers, E. 1983 Measurements of nonlinear interactions during natural transition of a symmetric wake. Phys. Fluids 26, 1402.Google Scholar
Miksad, R. W., Jones, F. L., Powers, E. J., Kim, Y. C. & Khadra, L. 1982 Experiments on the role of amplitude and phase modulations during transition to turbulence. J. Fluid Mech. 123, 1–29.Google Scholar
Saric, W. S. & Thomas, A. S. W. 1984 Experiments on the subharmonic route to turbulence in boundary layers. In Proc. IUTAM Symp. on Turbulence and Chaotic Phenomena in Fluids, Kyoto, Japan, Sept. 5–12.Google Scholar
Singer, B., Ferziger, J. & Reed, H. 1986 Investigation of the effects of initial disturbances on plane channel transition. AIAA Paper 86–0433.Google Scholar
Solis, R., Miksad, R. & Powers, E. 1986 Experiments on the influence of mean flow unsteadiness on the laminar—turbulent transition of a wake. In Proc. Tenth. Symp. on Fluids in Liquids, Rolla, Missouri.
Williams, D., Fasel, H. & Hama, F. R. 1984 Expermental determination of the three-dimensional vorticity field in the boundary-layer transition process. J. Fluid Mech. 149, 179.Google Scholar