Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T02:10:26.081Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact solutions of asymmetric baroclinic quasi-geostrophic dipoles with distributed potential vorticity

Published online by Cambridge University Press:  12 April 2019

A. Viúdez Open the ORCID record for A. Viúdez [Opens in a new window]
A. Viúdez*
Affiliation:
Department of Physical Oceanography and Technology, Institute of Marine Sciences, CSIC, Barcelona 08003, Spain
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An exact solution of a baroclinic three-dimensional vortex dipole in geophysical flows with constant background rotation and constant background stratification is provided under the quasi-geostrophic (QG) approximation. The motion of the dipole is unsteady but the potential vorticity contours move rigidly. The vortex comprises three potential vorticity anomaly modes, with a radial dependence given by the spherical Bessel functions and with azimuthal and polar dependences given by the spherical harmonics. The first mode, or spherical mode, accounts for the horizontal asymmetry of the vortex dipole and curvature of the dipole’s horizontal trajectory. The second mode, or dipolar mode, accounts for the speed of displacement of the vortex dipole. A third mode, or vertical tilting mode, accounts for the dipole’s vertical asymmetry. The QG vertical velocity field has two contributions: the first one is octupolar and depends entirely on the dipolar mode, and the second one is dipolar and depends on the nonlinear interaction between dipolar and vertical tilting modes.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Quasi-geostrophic flows Vortex Flows: Vortex dynamics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , R1
Copyright
© 2019 Cambridge University Press 

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

Ahlnäs, K., Royer, T. C. & George, T. H. 1987 Multiple dipole eddies in the Alaska Coastal Current detected with Landsat thematic mapper data. J. Geophys. Res. Oceans 92 (C12), 13041–13047.Google Scholar
Cavallini, F. & Crisciani, F. 2013 Quasi-Geostrophic Theory of Oceans and Atmosphere. Springer.Google Scholar
Chaplygin, S. A. 1903 One case of vortex motion in fluid. Trans. Phys. Sect. Imperial Moscow Soc. Friends of Natural Sciences 11 (N 2), 11–14.Google Scholar
Cunningham, P. & Keyser, D. 2000 Analytical and numerical modelling of jet streaks: barotropic dynamics. Q. J. R. Meteorol. Soc. 126 (570), 3187–3217.Google Scholar
Fedorov, K. N. & Ginsburg, A. I. 1989 Mushroom-like currents (vortex dipoles): one of the most widespread forms of non-stationary coherent motions in the ocean. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. Nihoul, J. C. J. & Jamart, B. M.), Elsevier Oceanography Series, vol. 50, pp. 1–14. Elsevier.Google Scholar
Flierl, G. R., Larichev, V. D., McWilliams, J. C. & Reznik, G. M. 1980 The dynamics of baroclinic and barotropic solitary eddies. Dyn. Atmos. Oceans 5 (1), 1–41.Google Scholar
Flierl, G. R., Stern, M. E. & Whitehead, J. A. 1983 The physical significance of modons: laboratory experiments and general integral constraints. Dyn. Atmos. Oceans 7, 233–263.Google Scholar
Kloosterziel, R. C., Carnevale, G. F. & Phillippe, D. 1993 Propagation of barotropic dipoles over topography in a rotating tank. Dyn. Atmos. Oceans 19, 65–100.Google Scholar
Meleshko, V. V. & van Heijst, G. J. F. 1994 On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid. J. Fluid Mech. 272, 157–182.Google Scholar
de Ruijter, W. P. M., van Aken, H. M., Beier, E. J., Lutjeharms, J. R. E., Matano, R. P. & Schouten, M. W. 2004 Eddies and dipoles around South Madagascar: formation, pathways and large-scale impact. Deep Sea Res. I 51, 383–400.Google Scholar
Velasco Fuentes, O. U. & van Heijst, G. J. F. 1995 Collision of dipolar vortices on a 𝛽 plane. Phys. Fluids 7, 2735–2750.Google Scholar
Viúdez, A. 2019 Azimuthal-mode solutions of two-dimensional Euler flows and the Chaplygin–Lamb dipole. J. Fluid Mech. 859, R1.Google Scholar
Voropayev, S. I. & Afanasyev, Ya. D. 1992 Two-dimensional vortex-dipole interactions in a stratified fluid. J. Fluid Mech. 236, 66–689.Google Scholar
Supplementary material: File

Viúdez supplementary material

Viúdez supplementary material 1

Download Viúdez supplementary material(File)
File 2.7 MB