Skip to main content

Tilt-induced instability of a stratified vortex


This experimental and theoretical study considers the dynamics and the instability of a Lamb–Oseen vortex in a stably stratified fluid. In a companion paper, it was shown that tilting the vortex axis with respect to the direction of stratification induces the formation of a rim of strong axial flow near a critical radius when the Froude number of the vortex is larger than one.

Here, we demonstrate that this tilt-induced flow is responsible for a three-dimensional instability. We show that the instability results from a shear instability of the basic axial flow in the critical-layer region. The theoretical predictions for the wavelength and the growth rate obtained by a local stability analysis of the theoretical critical-layer profile are compared to experimental measurements and a good agreement is observed. The late stages of the instability are also analysed experimentally. In particular, we show that the tilt-induced instability does not lead to the destruction of the vortex, but to a sudden decrease of its Froude number, through the turbulent diffusion of its core size, when the initial Froude number is close to 1. A movie is available with the online version of the paper.

Hide All
Abramowitz M. & Stegun I. A. 1965 Handbook of Mathematical Functions. Dover.
Billant P. & Chomaz J.-M. 2000 Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 418, 167188.
Boulanger N., Meunier P. & Le Dizès S. 2007 Structure of a stratified tilted vortex. J. Fluid Mech. 583, 443458.
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 J.-B. 2003 Instability of a columnar vortex in stratified fluid. Bull. Am. Phys. Soc. 48 (10), 164.
Crow S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 21722179.
Drazin P. G. & Reid W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Farmer D., Pawlowicz R. & Jiang R. 2002 Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean. Dyn. Atmos. Oceans 36, 4358.
Garnier E., Métais O. & Lesieur M. 1996 Instabilités primaire et secondaire d'un jet barocline. C. R. Acad. Sci., Paris B 323, 161168.
Hopfinger E. J. & van Heijst G. J. F. 1993 Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25, 241289.
Kerswell R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83113.
Meunier P. & Leweke T. 2003 Analysis and optimization of the error caused by high velocity gradients in particle image velocimetry. Exps. Fluids 35, 408421.
Nieman P. J., Shapiro M. A. & Fedor L. S. 1993 The life cycle of an extratropical marine cyclone. Part ii: mesoscale structure and diagnostics. Mon. Weather Rev. 121, 21772199.
Pawlak G., MacCready P., Edwards K. A. & McCabe R. 2003 Observations on the evolution of tidal vorticity at a stratified deep water headland. Geophys. Res. Lett. 30 (24), 2234.
Polavarapu S. M. & Peltier W. R. 1993 Formation of small-scale cyclones in numerical simulations of synoptic-scale baroclinic wave life cycles: secondary instability at the cusp. J. Atmos. Sci. 50, 10471057.
Schecter D. A., Montgomery M. T. & Reasor P. D. 2002 A theory for the vertical alignment of a quasigeostrophic vortex. J. Atmos Sci. 59 (2), 150168.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 13 *
Loading metrics...

Abstract views

Total abstract views: 103 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 17th November 2017. This data will be updated every 24 hours.