Skip to main content
×
Home
    • Aa
    • Aa

Tilt-induced instability of a stratified vortex

  • NICOLAS BOULANGER (a1), PATRICE MEUNIER (a1) and STÉPHANE LE DIZÈS (a1)
Abstract

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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.



S. C. Crow 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 21722179.

D. Farmer , R. Pawlowicz & R. Jiang 2002 Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean. Dyn. Atmos. Oceans 36, 4358.

E. J. Hopfinger & G. J. F. van Heijst 1993 Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25, 241289.

R. R. Kerswell 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83113.

P. Meunier & T. Leweke 2003 Analysis and optimization of the error caused by high velocity gradients in particle image velocimetry. Exps. Fluids 35, 408421.

P. J. Nieman , M. A. Shapiro & L. S. Fedor 1993 The life cycle of an extratropical marine cyclone. Part ii: mesoscale structure and diagnostics. Mon. Weather Rev. 121, 21772199.

G. Pawlak , P. MacCready , K. A. Edwards & R. McCabe 2003 Observations on the evolution of tidal vorticity at a stratified deep water headland. Geophys. Res. Lett. 30 (24), 2234.

S. M. Polavarapu & W. R. Peltier 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.

D. A. Schecter , M. T. Montgomery & P. D. Reasor 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? *
×
MathJax

Keywords: