Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-28T18:04:10.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Structure of a stratified tilted vortex

Published online by Cambridge University Press:  04 July 2007

NICOLAS BOULANGER ,
PATRICE MEUNIER  and
STÉPHANE LE DIZÈS
NICOLAS BOULANGER
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, CNRS/Universités Aix-Marseille I&II, 49, rue F. Joliot-Curie, B.P. 146, F-13384 Marseille cedex 13, France
PATRICE MEUNIER
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, CNRS/Universités Aix-Marseille I&II, 49, rue F. Joliot-Curie, B.P. 146, F-13384 Marseille cedex 13, France
STÉPHANE LE DIZÈS
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, CNRS/Universités Aix-Marseille I&II, 49, rue F. Joliot-Curie, B.P. 146, F-13384 Marseille cedex 13, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The structure of a columnar vortex in a stably stratified fluid is studied experimentally and theoretically when the vortex axis is slightly tilted with respect to the direction of stratification. When the Froude number of the vortex is larger than 1, we show that tilting induces strong density variations and an intense axial flow in a rim around the vortex. We demonstrate that these characteristics can be associated with a critical-point singularity of the correction of azimuthal wavenumber m = 1 generated by tilting where the angular velocity of the vortex equals the Brunt–Väisälä frequency of the stratified fluid. The theoretical structure obtained by smoothing this singularity using viscous effects (in a viscous critical-layer analysis) is compared to particle image velocimetry measurements of the axial velocity field and visualizations of the density field and a good agreement is demonstrated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 443 - 458
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
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, 167–188.CrossRefGoogle Scholar
Booker, J. R. & Bretherton, F. P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513–539.CrossRefGoogle Scholar
Boulanger, N., Meunier, P. & LeDizès, S. Dizès, S. 2007 Tilt-induced instability of a stratified vortex. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Cariteau, B. 2005 Etude de la stabilité et de l'interaction de cyclones intenses en fluide stratifié. PhD thesis, Université Joseph Fourier, Grenoble.Google Scholar
Cariteau, B. & Flór, J.-B. 2003 Instability of a columnar vortex in stratified fluid. Bull. Am. Phys. Soc. 48 (10), 164.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Farmer, D., Pawlowicz, R. & Jiang, R. 2002 Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean. Dyn. Atmos. Oceans 36, 43–58.CrossRefGoogle Scholar
Garnier, E., Métais, O. & Lesieur, M. 1996 Instabilités primaire et secondaire d'un jet barocline. C. R. Acad. Sci. Paris B 323, 161–168.Google Scholar
Hopfinger, E. J. & vanHeijst, G. J. F. Heijst, G. J. F. 1993 Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25, 241–289.CrossRefGoogle Scholar
Kerswell, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83–113.CrossRefGoogle Scholar
LeDizès, S. Dizès, S. 2000 Non-axisymmetric vortices in two-dimensional flows. J. Fluid Mech. 406, 175–198.Google Scholar
Lesieur, M., Métais, O. & Garnier, E. 2000 Baroclinic instability and severe storms. J. Turb. 1, 1–17.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
Maslowe, S. A. 1986 Critical layers in shear flows. Annu. Rev. Fluid Mech. 18, 405–432.CrossRefGoogle Scholar
Meunier, P. & Leweke, T. 2003 Analysis and optimization of the error caused by high velocity gradients in particle image velocimetry. Exps. 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
Neiman, 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, 2177–2199.2.0.CO;2>CrossRefGoogle Scholar
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, 2234.CrossRefGoogle Scholar
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, 1047–1057.2.0.CO;2>CrossRefGoogle Scholar