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Predicting the aftermath of vortex breakup in rotating flow

Published online by Cambridge University Press:  11 January 2011

G. F. CARNEVALE ,
R. C. KLOOSTERZIEL ,
P. ORLANDI  and
D. D. J. A. van SOMMEREN
G. F. CARNEVALE*
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
R. C. KLOOSTERZIEL
Affiliation:
School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, USA
P. ORLANDI
Affiliation:
Dipartimento di Meccanica e Aeronautica, University of Rome, ‘La Sapienza’, via Eudossiana 18, 00184 Roma, Italy
D. D. J. A. van SOMMEREN
Affiliation:
Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, the Netherlands
*
†Email address for correspondence: gcarnevale@ucsd.edu
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Abstract

A method for predicting the outcome of vortex breakup in a rotating flow is introduced. The vortices dealt with here are subject to both centrifugal and barotropic instabilities. The prediction of the aftermath of the breakup relies on knowing how both centrifugal and barotropic instabilities would equilibrate separately. A theoretical model for non-linear equilibration in centrifugal instability is wedded to two-dimensional simulation of barotropic instability to predict the final vortices that emerge from the debris of the original vortex. This prediction method is tested against three-dimensional Navier–Stokes simulations. For vortices in which a rapid centrifugal instability triggers a slower barotropic instability, the method is successful both qualitatively and quantitatively. The skill of the prediction method decreases as the time scales of the two instabilities become comparable.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Turbulent Flows: Turbulent Flows Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 90 - 119
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

‡

Present address: BP Institute and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0EZ, UK.

References

REFERENCES

Aristegui, J., Sangra, P., Hernandez-Leon, S., Canton, M., Hernandez-Guerra, A. & Kerling, J. L. 1994 Island-induced eddies in the Canary Islands. Deep Sea Res. 41, 1509–1525.CrossRefGoogle Scholar
Barba, L. A. & Leonard, A. 2007 Emergence and evolution of tripole vortices from net circulation initial conditions. Phys. Fluids 19, 017101.CrossRefGoogle Scholar
Bayly, B. J. 1988 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 56–64.CrossRefGoogle Scholar
Beckers, M. & van Heijst, G. J. F. 1998 The observation of a triangular vortex in a rotating fluid. Fluid Dyn. Res. 22, 265–279.CrossRefGoogle Scholar
Bennetts, D. A. & Hoskins, B. J. 1979 Conditional symmetric instability: a possible explanation for frontal rainbands. Q. J. R. Meteorol. Soc. 105, 945–962.Google Scholar
Carnevale, G. F., Briscolini, M., Kloosterziel, R. C. & Vallis, G. K. 1997 Three-dimensionally perturbed vortex tubes in a rotating flow. J. Fluid Mech. 341, 127–163.CrossRefGoogle Scholar
Carnevale, G. F. & Kloosterziel, R. C. 1994 Emergence and evolution of triangular vortices. J. Fluid Mech. 259, 305–331.CrossRefGoogle Scholar
Carton, X. J. 1992 The merger of homostrophic shielded vortices. Europhys. Lett. 18, 697–703.CrossRefGoogle Scholar
Carton, X. J., Fierl, G. R. & Polvani, L. M. 1989 The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9, 339–344.CrossRefGoogle Scholar
Carton, X. J. & Legras, B. 1994 The life-cycle of tripoles in two-dimensional incompressible flows. J. Fluid Mech. 267, 53–82.CrossRefGoogle Scholar
Carton, X. & McWilliams, J. C. 1989 Barotropic and baroclinic instabilities of axisymmetric vortices in a quasi-geostrophic model. In Mesoscale/Synotopic Coherent Structures in Geophysical Turbulence (ed. Nihoul, J. C. J. & Jamart, B. M.), pp. 225–244. Elsevier.CrossRefGoogle Scholar
D'Asaro, E. A. 1988 Generation of submesoscale vortices: a new mechanism. J. Geophys. Res. 93, 6685–6693.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Dritschel, D. G. 1986 The nonlinear evolution of rotating configurations of uniform vorticity. J. Fluid Mech. 172, 157–182.CrossRefGoogle Scholar
Dunkerton, T. J. 1981 On the inertial instability of the equatorial middle atmosphere. J. Atmos. Sci. 38, 2354–2365.2.0.CO;2>CrossRefGoogle Scholar
Flament, P., Lumpkin, R., Tournadre, J. & Armi, L. 2001 Vortex pairing in an unstable anticyclonic shear flow: discrete subharmonics of one pendulum day. J. Fluid Mech. 440, 401–409.CrossRefGoogle Scholar
Flierl, G. R. 1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349–388.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J. M. 2003 Three-dimensional instability of isolated vortices. Phys. Fluids 15 (8), 2113–2126.CrossRefGoogle Scholar
Hayashi, H., Shiotani, M. & Gille, J. C. 1998 Vertically stacked temperature disturbances near the equatorial stratopause as seen in cryogenic limb array etalon spectrometer data. J. Geophys. Res. 103, 19469–19483.CrossRefGoogle Scholar
van Heijst, G. J. F. & Kloosterziel, R. C. 1989 Tripolar vortices in a rotating fluid. Nature 338, 569–571.CrossRefGoogle Scholar
Kloosterziel, R. C. & Carnevale, G. F. 1992 Formal stability of circular vortices. J. Fluid Mech. 242, 249–278.CrossRefGoogle Scholar
Kloosterziel, R. C. & Carnevale, G. F. 1999 On the evolution and saturation of instabilities of two-dimensional isolated circular vortices. J. Fluid Mech. 388, 217–257.CrossRefGoogle Scholar
Kloosterziel, R. C., Carnevale, G. F. & Orlandi, P. 2007 a Inertial instability in rotating and stratified fluids: barotropic vortices. J. Fluid Mech. 583, 379–412.CrossRefGoogle Scholar
Kloosterziel, R. C. & van Heijst, G. J. F. 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 1–24.CrossRefGoogle Scholar
Kloosterziel, R. C., Orlandi, P. & Carnevale, G. F. 2007 b Saturation of inertial instability in rotating planar shear flows. J. Fluid Mech. 583, 413–422.CrossRefGoogle Scholar
Knox, J. A. 1997 Possible mechanisms for clear-air turbulence in strongly anticyclonic flows. J. Atmos. Sci. 125, 1251–1259.Google Scholar
Melander, M. V., McWilliams, J. C. & Zabusky, N. J. 1987 The axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation. J. Fluid Mech. 178, 137–159.CrossRefGoogle Scholar
Morel, Y. G. & Carton, X. J. 1994 Multipolar vortices in two-dimensional incompressible flows. J. Fluid Mech. 267, 23–51.CrossRefGoogle Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Kluwer.CrossRefGoogle Scholar
Orlandi, P. 2009 Energy spectra power laws and structures. J. Fluid Mech. 623, 353–374.CrossRefGoogle Scholar
Orlandi, P. & Carnevale, G. F. 1999 Evolution of isolated vortices in a rotating fluid of finite depth. J. Fluid Mech. 381, 239–269.CrossRefGoogle Scholar
Orlandi, P. & van Heijst, G. J. F. 1992 Numerical simulation of tripolar vortices in 2D flow. Fluid Dyn. Res. 9, 179–206.CrossRefGoogle Scholar
Rayleigh, Lord 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 57–70.Google Scholar
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–154.Google Scholar
Richards, K. J. & Edwards, N. R. 2003 Lateral mixing in the equatorial pacific: the importance of inertial instability. Geophys. Res. Lett. 30, 1–4.CrossRefGoogle Scholar
Sawyer, S. J. 1947 Notes on the theory of tropical cyclones. Q. J. R. Meteorol. Soc. 73, 101–126.CrossRefGoogle Scholar
Smyth, W. D. & McWilliams, J. C. 1998 Instability of an axisymmetric vortex in a stably stratified, rotating environment. Theor. Comput. Fluid Dyn. 11, 305–322.CrossRefGoogle Scholar
Stern, M. E. 1987 Horizontal entrainment and detrainment in large-scale eddies. J. Phys. Oceanogr. 17, 1688–1695.2.0.CO;2>CrossRefGoogle Scholar
Stone, P. H. 1966 On non-geostrophic stability. J. Atmos. Sci. 23, 390–400.2.0.CO;2>CrossRefGoogle Scholar
Stone, P. H. 1967 An application of baroclinic stability theory to the dynamics of the Jovian atmosphere. J. Atmos. Sci. 24, 642–652.2.0.CO;2>CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123, 402–414.CrossRefGoogle Scholar