Analysis of Stationary Points and Bifurcations
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 49-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

A dynamically consistent model of a meandering jet stream with two Rossby waves obtained using the law of conservation of potential vorticity is investigated. Stationary points are found in the phase space of advection equations and the type of their stability is determined analyti- cally. All topologically different flow regimes and their bifurcations are found for the stationary model (taking into account only the first Rossby wave). The results can be used in the study of Lagrangian transport, mixing, and chaotic advection in problems of cross-frontal transport in geophysical flows with meandering jets.
Keywords: stationary points, jet flow.
Mots-clés : separatrices reconnection
@article{ND_2023_19_1_a3,
     author = {A. A. Udalov and M. Yu. Uleysky and M. V. Budyansky},
     title = {Analysis of {Stationary} {Points} and {Bifurcations}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {49--58},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2023_19_1_a3/}
}
TY  - JOUR
AU  - A. A. Udalov
AU  - M. Yu. Uleysky
AU  - M. V. Budyansky
TI  - Analysis of Stationary Points and Bifurcations
JO  - Russian journal of nonlinear dynamics
PY  - 2023
SP  - 49
EP  - 58
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2023_19_1_a3/
LA  - en
ID  - ND_2023_19_1_a3
ER  - 
%0 Journal Article
%A A. A. Udalov
%A M. Yu. Uleysky
%A M. V. Budyansky
%T Analysis of Stationary Points and Bifurcations
%J Russian journal of nonlinear dynamics
%D 2023
%P 49-58
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2023_19_1_a3/
%G en
%F ND_2023_19_1_a3
A. A. Udalov; M. Yu. Uleysky; M. V. Budyansky. Analysis of Stationary Points and Bifurcations. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 49-58. http://geodesic.mathdoc.fr/item/ND_2023_19_1_a3/

[1] Uspekhi Fiz. Nauk, 176:11 (2006), 1177–1206 (Russian) | DOI | DOI

[2] Koshel, K. V. and Prants, S. V., Chaotic Advection in the Ocean, R Dynamics, Institute of Computer Science, Izhevsk, 2008, 360 pp. (Russian)

[3] Budyansky, M. V., Prants, S. V., and Uleysky, M. Yu., “Chaotic Advection in a Meandering Jet Flow”, Nelin. Dinam., 2:2 (2006), 165–180 (Russian) | DOI

[4] Dokl. Akad. Nauk, 439:6 (2011), 811–814 (Russian) | DOI

[5] Zh. Èksp. Teor. Fiz., 138:6 (2010), 1175–1188 (Russian) | DOI

[6] Lozier, M. S., Pratt, L. J., Rogerson, A. M., and Miller, P. D., “Exchange Geometry Revealed by Float Trajectories in the Gulf Stream”, J. Phys. Oceanogr., 27:11 (1997), 2327–2341 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[7] Aref, H., “Stirring by Chaotic Advection”, J. Fluid Mech., 143 (1984), 1–21 | DOI | MR | Zbl

[8] Sommeria, J., Meyers, S. D., and Swinney, H. L., “Laboratory Model of a Planetary Eastward Jet”, Nature, 337:6202 (1989), 58–61 | DOI

[9] Behringer, R. P., Meyers, S. D., and Swinney, H. L., “Chaos and Mixing in a Geostrophic Flow”, Phys. Fluids A, 3:5 (1991), 1243–1249 | DOI

[10] Solomon, T. H., Holloway, W. J., and Swinney, H. L., “Shear Flow Instabilities and Rossby Waves in Barotropic Flow in a Rotating Annulus”, Phys. Fluids A, 5:8 (1993), 1971–1982 | DOI

[11] del-Castillo-Negrete, D. and Morrison, P. J., “Chaotic Transport by Rossby Waves in Shear Flow”, Phys. Fluids A, 5:4 (1993), 948–965 | DOI | MR | Zbl

[12] Prants, S. V., Budyansky, M. V., and Uleysky, M. Yu., “Lagrangian Study of Surface Transport in the Kuroshio Extension Area Based on Simulation of Propagation of Fukushima-Derived Radionuclides”, Nonlinear Proc. Geophys., 21:1 (2014), 279–289 | DOI

[13] Prants, S. V., Budyansky, M. V., and Uleysky, M. Yu., “Lagrangian Simulation and Tracking of the Mesoscale Eddies Contaminated by Fukushima-Derived Radionuclides”, Ocean Sci., 13:3 (2017), 453–463 | DOI | MR

[14] Zaslavsky, G. M., The Physics of Chaos in Hamiltonian Systems, 2nd ed., Imperial College Press, London, 2007 | MR | Zbl