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Transitions and oscillatory regimes in two-layer geostrophic hetons and tripoles

Published online by Cambridge University Press:  01 December 2016

Biana Shteinbuch-Fridman ,
Viacheslav Makarov  and
Ziv Kizner
Biana Shteinbuch-Fridman
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
Viacheslav Makarov
Affiliation:
Instituto Politécnico Nacional, Centro Interdisciplinario de Ciencias Marinas, La Paz, Baja California Sur 23096, Mexico
Ziv Kizner*
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel
*
†Email address for correspondence: ziv.kizner@gmail.com
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Abstract

We investigate numerically the transitions and oscillatory regimes in two-layer quasigeostrophic hetons and tripoles composed of patches of uniform potential vorticity (PV). The contour-surgery algorithms are employed, in which either some symmetries are preserved, or asymmetric evolution of the vortex structures is allowed, induced by generally asymmetric numerical noise. The fluid layers are assumed equally thick. First, the evolution of hetons is considered. A heton, a steadily translating pair of vortices residing in different layers, is antisymmetric in the sense that the two PV patches are opposite in sign and symmetric in shape about the axis of translation. A feebly stable heton, when exposed to weak antisymmetric perturbations, responds by developing an oscillation, which culminates in a transition to a new, substantially robust oscillating heton. The results obtained reinforce our earlier findings regarding the modon-to-modon transition (Kizner et al., J. Fluid Mech., vol. 468, 2002, pp. 239–270; Kizner, Phys. Fluids, vol. 18 (5), 2006, 056601; Kizner, UTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (ed. Borisov et al.), IUTAM Bookseries, vol. 6, 2008, pp. 125–133. Springer) and clarify the transition mechanism. Asymmetric perturbations might cause a heton-to-tripole transition. Next we consider the transitions and oscillations in carousel tripoles exposed to weak, generally asymmetric perturbations. A carousel tripole is a steadily rotating centrally symmetric ensemble of three PV patches, with the central vortex being located in one layer and the two remaining, satellite vortices in the other layer. Depending on the tripoles’ size, hence also on the shape of the satellite vortices, three different types of transition are revealed, the transition to a ringed (shielded) monopole being one of them. Whereas the transition of a ringed monopole into a tripole is a known phenomenon, the reverse transition in baroclinic flows is detected for the first time.

JFM classification

Vortex Flows: Contour dynamics Geophysical and Geological Flows: Rotating flows Vortex Flows: Vortex breakdown
Type
Papers
Information
Journal of Fluid Mechanics , Volume 810 , 10 January 2017 , pp. 535 - 553
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© 2016 Cambridge University Press 

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