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Three-dimensional vortex dynamics in oscillatory flow separation

Published online by Cambridge University Press:  23 March 2011

MIGUEL CANALS  and
GENO PAWLAK
MIGUEL CANALS*
Affiliation:
Department of Engineering Science and Materials, University of Puerto Rico, Mayagüez, PR 00681, USA
GENO PAWLAK
Affiliation:
Department of Ocean and Resources Engineering, University of Hawaii, Honolulu, HI 96822, USA
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of coherent columnar vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is on the low Keulegan–Carpenter number range (0.2 < KC < 2), where KC is the ratio between the fluid particle excursion during half an oscillation cycle and the obstacle size, and for moderate Reynolds numbers (700 < Rev < 7500). For this parameter range, a periodic unidirectional vortex pair ejection regime is observed, in which the direction of vortex propagation is set by the initial conditions of the oscillations. These vortex pairs provide a direct mechanism for the transfer of momentum and enstrophy to the outer region of rough oscillating boundary layers. Vortices are observed to be short-lived relative to the oscillation time scale, which limits their propagation distance from the boundary. The instability mechanisms leading to vortex decay are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Dye visualizations reveal complex three-dimensional vortex interactions resulting in rapid vortex destruction. These visualizations suggest that one of the instabilities affecting the spanwise vortices is an elliptical instability of the strained vortex cores. This is supported by DPIV measurements which identify the spatial structure of the perturbations associated with the elliptical instability in the divergence field. We also identify regions in the periphery of the vortex cores which are unstable to the centrifugal instability. Vortex longevity is quantified via a vortex decay time scale, and the results indicate that vortex pair lifetimes are of the order of an oscillation period T.

JFM classification

Geophysical and Geological Flows: Coastal engineering Wakes/Jets: Separated flows Vortex Flows: Vortex breakdown
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 408 - 432
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Bayly, B. J. 1986 Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57 (17), 2160–2163.CrossRefGoogle ScholarPubMed
Bayly, J. 1988 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 56–64.CrossRefGoogle Scholar
Blondeaux, P., Scandura, P. & Vittori, G. 2004 Coherent structures in an oscillatory separated flow: numerical experiments. J. Fluid Mech. 518, 215–229.CrossRefGoogle Scholar
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Craik, A. D. D. & Criminale, W. O. 1986 Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier–Stokes equations. Proc. R. Soc. Lond. A 406, 13–26.Google Scholar
Eloy, C., Le Gal, P. & Le Dizès, S. 2000 Experimental study of the multipolar vortex instability. Phys. Rev. Lett. 85 (16), 3400–3403.CrossRefGoogle ScholarPubMed
Fincham, A. & Spedding, G. 1997 Low cost, high resolution DPIV for measurement of turbulent fluid flow. Exp. Fluids 23, 449–462.CrossRefGoogle Scholar
Graham, J. M. R. 1980 The forces on sharp-edged cylinders in oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 97, 331–346.CrossRefGoogle Scholar
Julien, S., Ortiz, S. & Chomaz, J.-M. 2004 Secondary instability mechanisms in the wake of a flat plate. Eur. J. Mech. B: Fluids 23, 157–165.CrossRefGoogle Scholar
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
Kloosterziel, R. C., Carnevale, G. F. & Orlandi, P. 2007 Inertial instability in rotating and stratified fluids: barotropic vortices. J. Fluid Mech. 583, 379–412.CrossRefGoogle Scholar
Krstic, R. V. & Fernando, H. J. S. 2001 The nature of rough-wall oscillatory boundary layers. J. Hydraul. Res. 39, 655–666.CrossRefGoogle Scholar
Landman, M. J. & Saffman, P. G. 1987 The three-dimensional instability of strained vortices in a viscous fluid. Phys. Fluids 30, 2339–2342.CrossRefGoogle Scholar
Le Dizès, S. & Laporte, F. 2002 Theoretical predictions for the elliptical instability in a two-vortex flow. J. Fluid Mech. 471, 169–201.CrossRefGoogle Scholar
Leblanc, S. & Cambon, C. 1997 On the three-dimensional instabilities of plane flows subjected to Coriolis force. Phys. Fluids 9 (5), 1307–1316.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1981 Oscillating flow over steep sand ripples. J. Fluid Mech. 107, 1–35.CrossRefGoogle Scholar
Mei, C. C. & Liu, P. L. 1993 Surface waves and coastal dynamics. Annu. Rev. Fluid Mech. 25, 215–240.CrossRefGoogle Scholar
Meunier, P. & Leweke, T. 2003 Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp. Fluids 35, 408–421.CrossRefGoogle Scholar
Meunier, P. & Leweke, T. 2005 Elliptic instability of a co-rotating vortex pair. J. Fluid Mech. 533, 125–159.CrossRefGoogle Scholar
Meunier, P., Leweke, T., Lebescond, R., Van Aughem, B. & Wang, C. 2004 DPIVsoft User Guide. IRPHE.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. A 346, 413–425.Google Scholar
Nichols, C. S. & Foster, D. L. 2007 Full-scale observations of wave-induced vortex generation over a rippled bed. J. Geophys. Res. 112 (C10015).CrossRefGoogle Scholar
Pradeep, D. S. & Hussain, F. 2001 Core dynamics of a strained vortex: instability and transition. J. Fluid Mech. 447, 247–285.CrossRefGoogle Scholar
Scandura, P., Vittori, G. & Blondeaux, P. 2000 Three-dimensional oscillatory flow over steep ripples. J. Fluid Mech. 412, 355–378.CrossRefGoogle Scholar
Singh, S. 1979 Forces on bodies in oscillatory flow. PhD thesis, University of London.Google Scholar
Sipp, D. & Jacquin, L. 2000 Three-dimensional centrifugal-type instabilities of two-dimensional flows in rotating systems. Phys. Fluids 12 (7), 1740–1748.CrossRefGoogle Scholar
Tao, L. & Thiagarajan, K. 2003 Low KC flow regimes of oscillating sharp edges I. Vortex shedding observation. Appl. Ocean. Res. 25, 21–35.CrossRefGoogle Scholar
Teinturier, S., Stegner, A., Didelle, H. & Viboud, S. 2010 Small-scale instabilities of an island wake flow in a rotating shallow-water layer. Dyn. Atmos. Oceans 49, 1–24.CrossRefGoogle Scholar
Tsai, C.-Y. & Widnall, S. E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721–733.CrossRefGoogle Scholar
Waleffe, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids 2 (1), 76–80.CrossRefGoogle Scholar
Williams, J. J., Metje, N., Coates, L. E. & Atkins, P. R. 2007 Sand suspension by vortex pairing. Geophys. Res. Lett. 34.CrossRefGoogle Scholar