Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T14:29:00.847Z Has data issue: false hasContentIssue false
  • English
  • Français

A new mechanism for oblique wave resonance in the ‘natural’ far wake

Published online by Cambridge University Press:  26 April 2006

C. H. K. Williamson  and
A. Prasad
C. H. K. Williamson
Affiliation:
Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA
A. Prasad
Affiliation:
Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.

With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 269 - 313
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775.Google Scholar
Cimbala, J. M. 1984 Large structure in the far wakes of two-dimensional bluff bodies. PhD thesis, Graduate Aeronautical Laboratories, California Institute of Technology.
Cimbala, J. M. & Krein, A. 1990 Effect of freestream conditions on the far wake of a cylinder. AIAA J. 28, 1369.Google Scholar
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1981 Wake instability leading to new large scale structures downstream of bluff bodies. Bull. Am. Phys. Soc. 26, 1256.Google Scholar
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1988 Large structure in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265.Google Scholar
Coles, D. 1985 The uses of coherent structure. AIAA Dryden lecture.
Corke, T. 1990 Efect of controlled resonant interactions and mode detuning on turbulent transition in boundary layers. In IUTAM Symp. on Laminar-Turbulent Transition (ed. D. Arnal & R. Michel). Springer.
Corke, T. 1993 Effect of mode detuning on far wake development. J. Fluid Mech. (to be submitted.)Google Scholar
Corke, T., Koga, D., Drubka, R. & Nagib, H. 1977 A new technique for introducing controlled sheets of streaklines in wind tunnels. IEEE Publication 77-CH 1251-8 AES.
Corke, T., Krull, J. D. & Ghassemi, M. 1992 Three-dimensional mode resonance in far wakes. J. Fluid Mech. 239, 99.Google Scholar
Corke, T. & Mangano, R. A. 1989 Resonant growth of three-dimensional modes in transitioning Blasius boundary layers. J. Fluid Mech. 209, 93.Google Scholar
Craik, A. D. D. 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393.Google Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Desruelle, D. 1983 Beyond the Karman vortex street. M.S. thesiS, Illinois Institute of Technology.
Eisenlohr, H. & Eckelmann, H. 1989 Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Phys. Fluids A 1, 189.Google Scholar
Gerrard, J. H. 1978 The wakes of cylindrical bluff bodies at low Reynolds number. Phil. Trans. R. Soc. Lond. A 288, 351.Google Scholar
Hama, F. R. 1957 Three-dimensional vortex pattern behind a circular cylinder. J. Aeronaut. Sci. 24, 156.Google Scholar
Hammache, M. 1991 APS Meeting. Bull. Am. Phys. Soc. 26, 1256.Google Scholar
Hammache, M. & Gharib, M. 1989 A novel method to promote parallel shedding in the wake of circular cylinders. Phys. Fluids A 1, 1611.Google Scholar
Hammache, M. & Gharib, M. 1991 An experimental study of the parallel and oblique vortex shedding from circular cylinders. J. Fluid Mech. 232, 567.Google Scholar
Hammache, M. & Gharib, M. 1992 On the evolution of three-dimensionalities in laminar bluff body wakes. In Proc. IUTAM Conf. on Bluff Body Wake Instabilities (ed. H. Eckelmann & J. M. R. Graham). Springer (to appear.)
Herbert, T. 1988 Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20, 487.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365.Google Scholar
Koenig, M., Eisenlohr, H., Eckelmann, H. 1990 The fine structure in the S-Re relationship of the laminar wake of a circular cylinder. Phys. Fluids A 2, 1607.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lasheras, J. C. & Meiburg, E. 1990 Three-dimensional vorticity modes in the wake of a flat plate. Phys. Fluids A 2, 371.Google Scholar
Mankbadi, R. R. 1993 Effect of mode detuning on laminar-turbulent transition in boundary layers. AIAA Aerospace Sci Conf., Reno, Nevada, Paper 93–0347.
Matsui, T. & Okude, M. 1981 Vortex pairing in a Karman vortex street. In Proc. Seventh Biennial Symp. on Turbulence, Rolla, Missouri.
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 Symp., Marseille, 1982. Springer.
Meiburg, E. 1987 On the role of subharmonic perturbations in the far wake. J. Fluid Mech. 177, 83.Google Scholar
Meiburg, E. & Lasheras, J. C. 1988 Experimental and numerical investigation of the three-dimensional transition in plane wakes. J. Fluid Mech. 190, 1.Google Scholar
Pierrehumbert, R. & Widnall, S. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59.Google Scholar
Raetz, R. E. 1959 A new cause of transition in fluid flows. Northrop Rep. NOR-59-383 (BLC-121.)
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.
Staffman, P. G. & Schatzman, J. C. 1982 Stability of a vortex street of finite vortices. J. Fluid Mech. 117, 171.Google Scholar
Squire, H. B. 1933 On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. R. Soc. Lond. A 142, 621.Google Scholar
Stuart, J. T. 1962 Nonlinear effects in hydrodynamic stability. In Proc. Tenth IUTAM Cong. of Applied Mech. (ed. F. Rolla & W. T. Koiter), pp. 91–97. Elsevier.
Taneda, S. 1959 Downstream development of wakes behind cylinders. J. Phys. Soc. Japan 14, 843.Google Scholar
Williamson, C. H. K. 1988a Denning a universal and continuous. Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31, 2742.Google Scholar
Williamson, C. H. K. 1988b The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31, 3165.Google Scholar
Williamson, C. H. K. 1989a Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579.Google Scholar
Williamson, C. H. K. 1989b Generation of periodic vortex dislocations due to a point disturbance in a planar wake. In The Gallery of Fluid Motion, Phys. Fluids A 1, 1444.Google Scholar
Williamson, C. H. K. 1991 Three-dimensional aspects and transition in the wake of a cylinder. In Turbulent Shear Flows (ed. F. Durst & J. Launder), pp. 173–194. Springer.
Williamson, C. H. K. 1992a The natural and forced formation of a spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393.Google Scholar
Williamson, C. H. K. 1992b Wave interactions in the far wake. In Proc. IUTAM Conf. on Bluff Body Wake Instabilities (ed. H. Eckelmann & J. M. R. Graham). Springer (to appear.)
Williamson, C. H. K. & Prasad, A. 1993a Oblique wave interactions in the far wake. Phys. Fluids A 5, 1854.Google Scholar
Williamson, C. H. K. & Prasad, A. 1993b Acoustic forcing of oblique wave resonance in the far wake. J. Fluid Mech. 256, 315.Google Scholar
Winant, C. D. & Brownand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237.Google Scholar