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On the role of subharmonic perturbations in the far wake

Published online by Cambridge University Press:  21 April 2006

E. Meiburg
E. Meiburg
Affiliation:
Institut fur Theoretische Strömungsmechanik, DFVLR, D-3400 Göttingen, West Germany Present address: Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
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Abstract

The possibility of an excitation of individual subharmonic perturbations in each of the shear layers forming the far wake is investigated numerically. Principal considerations allow for the existence of two equivalent subharmonic modes which by opposite routes can lead to a doubling of the wavelength in the wake. Since vortical disturbances in the far wake are amplified only convectively, the simultaneous existence of both modes in the flow field is possible, which could provide an explanation for the group structure observed experimentally in the far wake. These considerations also provide a logical explanation of the finding of a very regular vortex pairing process in forced wakes.

Two-dimensional numerical simulations assuming incompressible flow and almost inviscid dynamics illustrate the opposite developments of regions dominated by the two different modes and also confirm the possibility of a resulting group structure. As an important result it is demonstrated that, if vortex pairing plays an important role in the growth of the far-wake structure, this does not have to be related to the excitation of the subharmonic peak in the frequency spectrum. Quite the contrary, it is to be expected that the subharmonic itself is of minor importance and that instead a small frequency and its multiples related to the group structure of the flow dominate the spectrum. In the light of these considerations measurements by Cimbala (1984) are discussed and frequency spectra recorded by him are analysed more closely. Various properties of these spectra seem to indicate that vortex pairing might be significant with respect to the evolution of the far-wake structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 83 - 107
Copyright
© 1987 Cambridge University Press

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References

Aref, H. & Siggia, H., 1981 Evolution and breakdown of a vortex street in two dimensions. J. Fluid Mech. 109, 435–463.Google Scholar
Breidenthal, R. 1980 Response of plane shear layers and wakes to strong three-dimensional disturbances. Phys. Fluids 23, 1929–1934.Google Scholar
Cimbala, J. M. 1984 Large structure in the far wakes of two-dimensional bluff bodies. Ph.D. thesis, California Institute of Technology.
Corcos, G. M. & Sherman, F. S. 1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow. J. Fluid Mech. 139, 29–65.Google Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Koshigoe, S., Yang, V. & Culick, F. E. C. 1984 Calculations of interaction of acoustic waves with a two-dimensional free shear layer. AIAA paper 85–0043.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Leonard, A. 1980 Vortex methods for flow simulation. J. Comp. Phys. 37, 289–335.Google Scholar
Leonard, A. 1985 Computing thre-dimensional incompressible flows with vortex elements. Ann. Rev. Fluid Mech. 17, 523–559.Google Scholar
Matsui, T. & Okude, M. 1983 Formation of the secondary vortex street in the wake of a circular cylinder. In Structure of Complex Turbulent Shear Flow, IUTAM Symposium, Marseille, 1982 (ed. R. Dumas & L. Fulachier). Springer.
Meiron, D. I., Saffman, P. G. & Schatzman, J. C. 1984 The linear two-dimensional stability of inviscid vortex streets of finite-cored vortices. J. Fluid Mech. 147, 187–212.Google Scholar
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 A numerical simulation of Kelvin-Helmholtz waves of finite amplitudes. J. Fluid Mech. 73, 215–240.Google Scholar
Riley, J. J. & Metcalfe, R. W. 1980 Direct numerical simulation of a perturbed, turbulent mixing layer. AIAA paper 80–0274.Google Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 1349–1357.Google Scholar
Sirovich, L. 1985 The Kármán vortex trail and flow behind a circular cylinder. Phys. Fluids 28, 2723–2726.Google Scholar
Taneda, S. 1959 Downstream development of the wakes behind cylinders. J. Phys. Soc. Japan 14, 843–848.Google Scholar
Townsend, A. A. 1979 Flow patterns of large eddies in a wake and in a boundary layer. J. Fluid Mech. 95, 515–537.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar