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Structure and entrainment in the plane of symmetry of a turbulent spot

Published online by Cambridge University Press:  12 April 2006

Brian Cantwell ,
Donald Coles  and
Paul Dimotakis
Brian Cantwell
Affiliation:
Institute of Technology, Pasadena, California
Donald Coles
Affiliation:
Institute of Technology, Pasadena, California
Paul Dimotakis
Affiliation:
Institute of Technology, Pasadena, California
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Abstract

Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as $\psi = U^2_{\infty}tg(\xi, \eta) $ in conical similarity co-ordinates ζ = x/U∞t and η = y/U∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U∞. A second stable focus with celerity 0·64U∞ also appears near the wall at the rear of the spot.

Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Görtler type in the sublayer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 4 , 29 August 1978 , pp. 641 - 672
Copyright
© 1978 Cambridge University Press

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References

Bevilaqua, P. M. & Lykoudis, P. S. 1971 Mechanism of entrainment in turbulent wakes. A.I.A.A. J. 9, 1657–1659.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids Suppl. 20, S243–S252.Google Scholar
Cantwell, B. J. 1978 Similarity transformations for the two-dimensional, unsteady, stream-function equation. J. Fluid Mech. 85, 257–271.Google Scholar
Coles, D. 1962 The turbulent boundary layer in a compressible fluid. Rand Corp. Rep. R-403-PR, appendix A.Google Scholar
Coles, D. & Barker, S. J. 1975 Some remarks on a synthetic turbulent boundary layer. In Turbulent Mixing in Nonreactive and Reactive Flows (ed. S. N. B. Murthy), pp. 285–292. Plenum.
Corrsin, S. & Kistler, A. L. 1954 The free-stream boundaries of turbulent flows. N.A.C.A. Tech. Note no. 3133. (See also N.A.C.A. Tech. Rep. no. 1244, 1955.)Google Scholar
Dimotakis, P. E. 1976 Single scattering particle laser-Doppler measurements of turbulence. AGARD Conf. Proc. 193, pp. 10.1–10.14.Google Scholar
Dimotakis, P. E. & Lang, D. B. 1974 Single scattering particle laser-Doppler velocimetry. Bull. Am. Phys. Soc. II 19, 1145.Google Scholar
Elder, J. W. 1960 An experimental investigation of turbulent spots and breakdown to turbulence. J. Fluid Mech. 9, 235–246.Google Scholar
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer. Part I. J. Aero. Sci. 18, 490–498.Google Scholar
Hama, F. R. 1962 Streaklines in perturbed shear flow. Phys. Fluids 5, 644–650.Google Scholar
Hunt, J. C. R. & Mulhearn, P. J. 1973 Turbulent dispersion from sources near two-dimensional obstacles. J. Fluid Mech. 61, 245–274.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.Google Scholar
Kovasznay, L. S. G. 1949 Technique for the optical measurement of turbulence in high speed flow. Proc. Heat Transfer Fluid Mech. Inst., Berkeley, pp. 211–222.Google Scholar
Kreid, D. K. 1974 Laser-Doppler velocimeter measurements in non-uniform flow: error estimates. Appl. Optics 13, 1872–1881.Google Scholar
Mclaughlin, D. K. & Tiederman, W. G. 1973 Biasing correction for individual realization of laser anemometer measurements in turbulent flows. Phys. Fluids 16, 2082–2088.Google Scholar
Mayo, W. T. 1974 A discussion of limitations and extensions of power spectrum estimation with burst-counter LDV systems. Proc. 2nd Int. Workshop Laser Velocimetry, Purdue Univ. (ed. H. D. Thompson & W. H. Stevenson), vol. 1, pp. 90–101.Google Scholar
Meyer, K. A. & Kline, S. J. 1961 A visual study of the flow model in the later stages of laminar–turbulent transition on a flat plate. Stanford Univ., Dept. Mech. Engng Rep. MD-7.Google Scholar
Perry, A. E. & Fairlie, B. D. 1974 Critical points in flow patterns. Adv. in Geophys. B 18, 299–315.Google Scholar
Schubauer, G. B. & Klebanoff, P. S. 1955 Contributions on the mechanics of boundary-layer transition. N.A.C.A. Tech. Note no. 3489. (See also N.A.C.A. Tech. Rep. no. 1289, 1956.)Google Scholar
Smith, A. M. O. 1954 Improved solutions of the Falkner and Skan boundary-layer equation. Inst. Aero. Sci., S. M. F. Fund. paper FF-10.Google Scholar
Turner, J. S. 1964 The flow into an expanding spherical vortex. J. Fluid Mech. 18, 195–208.Google Scholar
Wygnanski, I., Haritonidis, J. H. & Kaplan, R. E. 1978 On a Tollmien–Schlichting wave packet produced by a turbulent spot. Submitted to J. Fluid Mech.Google Scholar
Wygnanski, I., Sokolov, N. & Friedman, D. 1976 On the turbulent ‘spot’ in a boundary layer undergoing transition. J. Fluid Mech. 78, 785–819.Google Scholar