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Eduction of large-scale organized structures in a turbulent plane wake

Published online by Cambridge University Press:  21 April 2006

A. K. M. Fazle Hussain  and
M. Hayakawa
A. K. M. Fazle Hussain
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77004, USA
M. Hayakawa
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77004, USA Permanent address: Department of Mechanical Engineering II, Hokkaido University, Sapporo 060, Japan.
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Abstract

Large-scale organized structures in the turbulent plane wake of a circular cylinder are investigated in air up to a downstream distance of 40d at a Reynolds number of Red = 1.3 × 104; d is the cylinder diameter. Velocity signals from a linear transverse rake of 8 X-wires are sampled simultaneously to calculate the instantaneous span wise vorticity. We have appropriately smoothed the temporal traces of vorticity to obtain time evolutions (including the transverse displacement, sign, strength and size distributions) of organized structures identified by vorticity contour maps. The periodicity of the initial structures is rapidly lost: dispersion in streamwise spacing, transverse displacement, strength and size of structures increases with increasing downstream distance.

Particular emphasis is placed on examining alternative general schemes for educing coherent structures in natural or unexcited turbulent shear flows, especially in their fully developed states. The optimal eduction scheme employed involves centring the rake at the most probable transverse location of centres of advected structures and accepting those structures that: (i) are centred at the midpoint of the rake, (ii) have a peak value of (smoothed) vorticity of a given sign above a specified level, and (iii) have streamwise and transverse extents of the (smoothed) vorticity contours above a specified size. From successive accepted structure signatures the instants of occurrence of structure centres (i.e. smoothed vorticity peaks) are identified. Un-smoothed signals are then time-aligned with respect to these instants and ensemble averaged to educe coherent structure and incoherent turbulence characteristics. Further enhancement is achieved by iteratively improving the time-alignment by maximizing the cross-correlation of individual structure vorticity with the ensemble-averaged vorticity and by discarding structures that require excessive time shifts or that produce significantly weak peak correlation values.

Following this optimal scheme, large-scale coherent structures have been educed in the fully turbulent wake. The average structure centre is found to be closer to the wake centreline than the half-width location, and the structure size does not increase in proportion to the wake width, suggesting that transverse wandering of structures (including their three-dimensionality) increases significantly with increasing downstream distance. The various flow properties associated with coherent and incoherent turbulence, and the coherent structure dynamics, in particular the role of vortex stretching (at the saddle) in turbulence production and mixing, are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 193 - 229
Copyright
© 1987 Cambridge University Press

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References

Bernal, L. P. 1981 The coherent structure of turbulent mixing layers. I. Similarity of primary vortex structure. II. Secondary streamwise vortex structure. Ph.D. thesis, California Institute of Technology.
Bernal, L. P. & Roshko, A. 1986 J. Fluid Mech. 170, 499.
Blackwelder, R. F. & Kaplan, R. E. 1976 J. Fluid Mech. 76, 89.
Boisson, H. C. 1983 Dévelopment de structures organizées turbulentes à travers l'exemple du sillage d'un cylindre circulaire. Ph.D. thesis, IMF, Toulouse, France
Breidenthal, R. E. 1980 Phys. Fluids 23, 1929.
Browand, F. K. 1980 Lecture at APS Meeting, Cornell University.
Beowand, F. K. & Troutt, T. R. 1985 J. Fluid Mech. 158, 489.
Browand, F. K. & Weidman, P. D. 1976 J. Fluid Mech. 76, 127.
Brown, G. L. & Roshko, A. 1974 J. Fluid Mech. 64, 775.
Bruun, H. H. 1977 J. Fluid Mech. 83, 641.
Cantwell, B. & Coles, D. 1983 J. Fluid Mech. 136, 321.
Cantwell, B., Coles, D. & Dimotakis, P. 1978 J. Fluid Mech. 87, 641.
Castro, I. 1971 J. Fluid Mech. 46, 599.
Cimbala, J. M. 1984 Large structure in the far wakes of two dimensional bluff bodies. Ph.D. thesis, California Institute of Technology.
Cimbala, J. M., Nagib, H. & Roshko, A. 1981 Bull. Am. Phys. Soc. 26, 1256.
Coles, D. 1981 Proc. Int. Acad. Sci. (Engng Sci.) 4, 111.
Coles, D. 1983 Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), p. 397. North-Holland.
Crow, C. & Champagne, F. H. 1971 J. Fluid Mech. 48, 547.
Desruelle, D. 1983 Beyond the Kármán vortex street. M.S. thesis. Illinois Institute of Technology.
Durgin, W. & Karlsson, B. 1971 J. Fluid Mech. 48, 507.
Fiedler, H. E., Dziomba, B., Mensing, P. & Rösgen, T. 1981 In Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, p. 219. Springer.
Gerrard, H. 1966 J. Fluid Mech. 25, 143.
Grant, H. L. 1958 J. Fluid Mech. 4, 149.
Gupta, A., Laufer, J. & Kaplan, R. 1971 J. Fluid Mech. 50, 493.
Hayakawa, M. & Hussain, A. K. M. F. 1985 Turbulent Shear Flows V, p. 4.38. Cornell University (also Rep. FM-20, University of Houston).
Hayakawa, M. & Hussain, A. K. M. F. 1986 Proc. 3rd Asian Cong. Fluid Mech. (ed. T. Matsui), p. 206. H. Sato.
Hayakawa, M., Tso, J., Kleis, S. J. & Hussain, A. K. M. F. 1983 Bull. Am. Phys. Soc. 28, 1370.
Husain, H. S. 1984 An experimental investigation of unexcited and excited elliptic jets. Ph.D. thesis, University of Houston.
Hussain, A. K. M. F. 1981a In Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, p. 252. Springer.
Hussain, A. K. M. F. 1981b Proc. Ind. Acad. Sci. (Eng. Sc.) 4, 129.
Hussain, A. K. M. F. 1983a Phys. Fluids 26, 2816.
Hussain, A. K. M. F. 1983b Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), p. 453. North-Holland.
Hussain, A. K. M. F. 1986 J. Fluid Mech. 173, 303.
Hussain, A. K. M. F. & Clark, A. R. 1981 J. Fluid Mech. 104, 493.
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1980 J. Fluid Mech. 101, 493.
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1982 Rep. FM-14, University of Houston (also J. Fluid Mech. 159, 85 (1985)).
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1985 J. Fluid Mech. 159, 85.
Jimenez, J., Cogollos, M. & Bernal, L. P. 1985 J. Fluid Mech. 152, 125.
Keffer, J. 1965 J. Fluid Mech. 22, 135.
Kleis, S. J., Hussain, A. K. M. F. & Sokolov, M. 1981 J. Fluid Mech. 111, 87.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Konrad, J. H. 1977 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Ph.D. thesis. California Institute of Technology.
Kunen, J. M. G., Ooms, & Vink, P. J. J. 1983 Symp. Turbulence, p. 37 University of Missouri-Rolla.
Matsui, T. & Okude, M. 1981 Turbulence in Liquids, p. 303 University of Missouri-Rolla.
Matsui, T. & Okude, M. 1983 In Structure of Complex Turbulent Shear Flow (ed. R. Dumas & L. Fulachier), p. 156. Springer.
Metcalfe, R., Hussain, A. K. M. F., Menon, S. & Hayakawa, M. 1987 Fifth Symp. Turbulent Shear Flow, Vol. 5 (ed. F. Durst et al.), p. 110, Springer.
Mumford, J. C. 1983 J. Fluid Mech. 137, 447.
Nishioka, M., Asai, M. & Iida, S. 1981 In Transition and Turbulence (ed. R. E. Meyer), p. 113. Academic.
Nishioka, M. & Sato, H. 1978 J. Fluid Mech. 89, 49.
Oshima, Y. & Asaka, S. 1977 J. Phys. Soc. Japan 42, 708.
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 J. Fluid Mech. 73, 215.
Perry, A. E., Chong, M. S. & Lim, T. T. 1982 J. Fluid Mech. 116, 77.
Perry, A. E. & Watmuff, J. H. 1981 J. Fluid Mech. 103, 33.
Roshko, A. 1954 NASA TN 3169.
Sato, H. 1983 Proc. 2nd Asian Cong. Fluid Mech. (ed. T. Deyan), p. 7. Beijing, China: Science.
Savill, A. M. 1983 In Structure of Complex Turbulent Shear Flow (ed. R. Dumas & L. Fulachier), p. 185. Springer.
Sreenivasan, K. R. & Narasimha, R. 1982 Trans. ASME I: J. Fluids Engng 104, 167
Takaki, R. & Hussain, A. K. M. F. 1985 Fifth Symp. Turbulent Shear Flow, p. 3.19. Cornell University.
Taneda, S. 1959 J. Phys. Soc. Japan 14, 843.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1979 J. Fluid Mech. 95, 515.
Tritton, D. J. 1959 J. Fluid Mech. 6, 547.
Tso, J. 1983 Coherent structures in a fully-developed turbulent axisymmetic jet. Ph.D. thesis, Johns Hopkins University.
Winant, C. D. & Browand, F. K. 1974 J. Fluid Mech. 63, 237.
Wlezien, R. 1981 The evolution of the low-wavenumber structure in a turbulent wake. Ph.D. thesis, IIT, Chicago
Wygnanski, I., Champagne, F. & Marasli, B. 1986 J. Fluid Mech. 168, 31.
Wygnanski, I., Sokolov, M. & Friedman, D. 1975 J. Fluid Mech. 69, 283.
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 J. Fluid Mech. 78, 785.
Yule, A. J. 1978 J. Fluid Mech. 89, 413.
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 J. Fluid Mech. 112, 379.
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1984 J. Fluid Mech. 138, 325.
Zilberman, M., Wygnanski, E. & Kaplan, R. E. 1977 Phys. Fluids Suppl. 20, S258.
Zdravkovich, M. M. 1968 J. Fluid Mech. 32, 339.