×

Exact solutions of asymmetric baroclinic quasi-geostrophic dipoles with distributed potential vorticity. (English) Zbl 1415.86024

Summary: 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.

MSC:

86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
76B65 Rossby waves (MSC2010)
76B47 Vortex flows for incompressible inviscid fluids
76U05 General theory of rotating fluids
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Ahlnäs, K.; Royer, T. C.; George, T. H., Multiple dipole eddies in the Alaska Coastal Current detected with Landsat thematic mapper data, J. Geophys. Res. Oceans, 92, C12, 13041-13047, (1987)
[2] Cavallini, F.; Crisciani, F., Quasi-Geostrophic Theory of Oceans and Atmosphere, (2013), Springer
[3] Chaplygin, S. A., One case of vortex motion in fluid, Trans. Phys. Sect. Imperial Moscow Soc. Friends of Natural Sciences, 11, N 2, 11-14, (1903)
[4] Cunningham, P.; Keyser, D., Analytical and numerical modelling of jet streaks: barotropic dynamics, Q. J. R. Meteorol. Soc., 126, 570, 3187-3217, (2000)
[5] Fedorov, K. N. & Ginsburg, A. I.1989Mushroom-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.), , vol. 50, pp. 1-14. Elsevier.
[6] Flierl, G. R.; Larichev, V. D.; Mcwilliams, J. C.; Reznik, G. M., The dynamics of baroclinic and barotropic solitary eddies, Dyn. Atmos. Oceans, 5, 1, 1-41, (1980)
[7] Flierl, G. R.; Stern, M. E.; Whitehead, J. A., The physical significance of modons: laboratory experiments and general integral constraints, Dyn. Atmos. Oceans, 7, 233-263, (1983)
[8] Kloosterziel, R. C.; Carnevale, G. F.; Phillippe, D., Propagation of barotropic dipoles over topography in a rotating tank, Dyn. Atmos. Oceans, 19, 65-100, (1993)
[9] Meleshko, V. V.; Van Heijst, G. J. F., On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid, J. Fluid Mech., 272, 157-182, (1994) · Zbl 0819.76018
[10] De Ruijter, W. P. M.; Van Aken, H. M.; Beier, E. J.; Lutjeharms, J. R. E.; Matano, R. P.; Schouten, M. W., Eddies and dipoles around South Madagascar: formation, pathways and large-scale impact, Deep Sea Res. I, 51, 383-400, (2004)
[11] Velasco Fuentes, O. U.; Van Heijst, G. J. F., Collision of dipolar vortices on a 𝛽 plane, Phys. Fluids, 7, 2735-2750, (1995) · Zbl 1027.76512
[12] Viúdez, A., Azimuthal-mode solutions of two-dimensional Euler flows and the Chaplygin-Lamb dipole, J. Fluid Mech., 859, R1, (2019) · Zbl 1415.76103
[13] Voropayev, S. I.; Afanasyev, Ya. D., Two-dimensional vortex-dipole interactions in a stratified fluid, J. Fluid Mech., 236, 66-689, (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.