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Instability of a vertical columnar vortex in a stratified fluid

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Abstract

In this article, we study experimentally the evolution of a vertical columnar vortex in a stratified fluid. Three different measurement techniques are used. Particle image velocimetry allows us to monitor the time evolution of the characteristics of the vortex (Froude and Reynolds numbers). Dye visualizations reveal the existence of an instability for Froude numbers smaller than one, which creates an undulation of the vortex centerline. Synthetic schlieren visualization shows that the density structure of the unstable mode is very similar to the structure found recently numerically for the radiative instability of a Lamb–Oseen vortex (Riedinger et al. in J Fluid Mech, 2010). The experimental stability diagram and unstable wavelengths are compared with these numerical results. A secondary instability associated with the presence of critical layers is also observed for Froude numbers larger than one.

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References

  • Billant P, Chomaz JM (2000a) Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J Fluid Mech 418:167–188

    Article  MATH  MathSciNet  Google Scholar 

  • Billant P, Chomaz JM (2000b) Theoretical analysis of the zigzag instability of a columnar vortex pair in a strongly stratified fluid. J Fluid Mech 419:29–63

    Article  MATH  MathSciNet  Google Scholar 

  • Billant P, Le Dizès S (2009) Waves on a columnar vortex in a strongly stratified fluid. Phys Fluids 21 (106602)

  • Boulanger N, Meunier P, Le Dizès S (2007) Structure of a tilted stratified vortex. J Fluid Mech 583:443–458

    Article  MATH  MathSciNet  Google Scholar 

  • Boulanger N, Meunier P, Le Dizès S (2008) Instability of a tilted vortex in stratified fluid. J Fluid Mech 596:1–20

    Article  MATH  MathSciNet  Google Scholar 

  • Cariteau B (2005) Etude de la stabilité et de l’interaction de cyclones intenses en fluide stratifié. PhD thesis, Université Joseph Fourier, Grenoble

  • Cariteau B, Flór JB (2006) An experimental investigation on elliptical instability of a strongly asymmetric vortex pair in a stable density stratification. Nonlin Processes Geophys 13:1–9

    Article  Google Scholar 

  • Crow SC (1970) Stability theory for a pair of trailing vortices. AIAA J 8(12):2172–2179

    Article  Google Scholar 

  • Drazin PG, Reid WH (1981) Hydrodynamic stability. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Fabre D, Sipp D, Jacquin L (2006) The Kelvin waves and the singular modes of the Lamb-Oseen vortex. J Fluid Mech 551:235–274

    Article  MATH  MathSciNet  Google Scholar 

  • Ford R (1994) The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water. J Fluid Mech 280:303–334

    Article  MATH  MathSciNet  Google Scholar 

  • Kelvin L (1880) Vibrations of a columnar vortex. Phil Mag 10:155–168

    Google Scholar 

  • Le Bars M, Le Gal P (2007) Experimental analysis of the stratorotational instability in a cylindrical Couette flow. Phys Rev Lett 99 (064502)

  • Le Dizès S, Billant P (2009) Radiative instability in stratified vortices. Phys Fluids 21 (096602)

  • Le Dizès S, Riedinger X (2010) The strato-rotational instability of keplerian and Taylor-Couette flows. J Fluid Mech (submitted)

  • Leibovich S, Brown S, Patel Y (1986) Bending waves on inviscid columnar vortices. J Fluid Mech 173:595–624

    Article  MATH  Google Scholar 

  • Meunier P, Leweke T (2003) Analysis and optimization of the error caused by high velocity gradients in particle image velocimetry. Exp Fluids 35(5):408–421

    Article  Google Scholar 

  • Molemaker MJ, McWilliams JC, Yavneh I (2001) Instability and equilibration of centrifugally stable stratified Taylor-Couette flow. Phys Rev Lett 86:5270–5273

    Article  Google Scholar 

  • Plougonven R, Zeitlin V (2002) Internal gravity wave emission from a pancake vortex: an example of wave-vortex interaction in strongly stratified flows. Phys Fluids 14:1259–1268

    Article  MATH  MathSciNet  Google Scholar 

  • Riedinger X, Le Dizès S, Meunier P (2010) Viscous stability properties of a Lamb-Oseen vortex in a stratified fluid. J Fluid Mech (in press)

  • Schecter DA, Montgomery MT (2004) Damping and pumping of a vortex Rossby wave in a monotonic cyclone: critical layer stirring versus inertia–buoyancy wave emission. Phys Fluids 16:1334–1348

    Article  MathSciNet  Google Scholar 

  • Sutherland BR, Dalziel SB, Hughes GO, Linden PF (1999) Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder. J Fluid Mech 390:93–126

    Article  MATH  Google Scholar 

  • Thomas P, Auerbach D (1994) The observation of the simultaneous development of a long and short-wave instability mode on a vortex pair. J Fluid Mech 265:289–302

    Article  Google Scholar 

  • Withjack E, Chen C (1974) An experimental study of Couette instability of stratified fluids. J Fluid Mech 66:725–737

    Article  Google Scholar 

  • Yavneh I, McWilliams J, Molemaker M (2001) Non-axisymmetric instability of centrifugally stable stratified Taylor–Couette flow,. J Fluid Mech 448:1–21

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. IRPHE, CNRS & Aix-Marseille University, 49, Rue F. Joliot Curie, 13013, Marseille, France

    Xavier Riedinger, Patrice Meunier & Stéphane Le Dizès

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  1. Xavier Riedinger
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  2. Patrice Meunier
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  3. Stéphane Le Dizès
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Riedinger, X., Meunier, P. & Le Dizès, S. Instability of a vertical columnar vortex in a stratified fluid. Exp Fluids 49, 673–681 (2010). https://doi.org/10.1007/s00348-010-0833-0

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  • DOI: https://doi.org/10.1007/s00348-010-0833-0

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