The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field
We study the evolution of N -point vortices in ring formation embedded in a background flowfield that initially corresponds to solid-body rotation on a sphere. The evolution of the point vortices is tracked numerically as an embedded dynamical system along with the M contours which separate strips o...
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crroyalsociety:10.1098/rspa.2006.1802 2024-06-02T08:11:51+00:00 The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field Newton, Paul K Sakajo, Takashi 2007 http://dx.doi.org/10.1098/rspa.2006.1802 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2006.1802 https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2006.1802 en eng The Royal Society https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 463, issue 2080, page 961-977 ISSN 1364-5021 1471-2946 journal-article 2007 crroyalsociety https://doi.org/10.1098/rspa.2006.1802 2024-05-07T14:16:08Z We study the evolution of N -point vortices in ring formation embedded in a background flowfield that initially corresponds to solid-body rotation on a sphere. The evolution of the point vortices is tracked numerically as an embedded dynamical system along with the M contours which separate strips of constant vorticity. The full system is a discretization of the Euler equations for incompressible flow on a rotating spherical shell, hence a ‘barotropic’ model of the one-layer atmosphere. We describe how the coupling creates a mechanism by which energy is exchanged between the ring and the background, which ultimately serves to break up the structure. When the centre-of-vorticity vector associated with the ring is initially misaligned with the axis of rotation of the background field, it sets up the propagation of Rossby waves around the sphere which move retrograde to the solid-body rotation. These waves pass energy to the ring (in the case when the solid-body field and the ring initially co-rotate) or extract energy from the ring (when the solid-body field and the ring initially counter-rotate), hence the Hamiltonian and the centre-of-vorticity vector associated with the N -point vortices are no longer conserved as they are for the one-way coupled model described by Newton & Shokraneh. In the first case, energy is transferred to the ring, the length of the centre-of-vorticity vector increases, while its tip spirals in a clockwise manner towards the North Pole. The ring stays relatively intact for short times, but ultimately breaks-up on a longer time-scale. In the latter case, energy is extracted from the ring, the length of the centre-of-vorticity vector decreases while its tip spirals towards the North Pole and the ring loses its coherence more quickly than in the co-rotating case. The special case where the ring is initially oriented so that its centre-of-vorticity vector is perpendicular to the axis of rotation is also examined as it shows how the coupling to the background field breaks this symmetry. In ... Article in Journal/Newspaper North Pole The Royal Society North Pole Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463 2080 961 977 |
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Open Polar |
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The Royal Society |
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crroyalsociety |
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English |
description |
We study the evolution of N -point vortices in ring formation embedded in a background flowfield that initially corresponds to solid-body rotation on a sphere. The evolution of the point vortices is tracked numerically as an embedded dynamical system along with the M contours which separate strips of constant vorticity. The full system is a discretization of the Euler equations for incompressible flow on a rotating spherical shell, hence a ‘barotropic’ model of the one-layer atmosphere. We describe how the coupling creates a mechanism by which energy is exchanged between the ring and the background, which ultimately serves to break up the structure. When the centre-of-vorticity vector associated with the ring is initially misaligned with the axis of rotation of the background field, it sets up the propagation of Rossby waves around the sphere which move retrograde to the solid-body rotation. These waves pass energy to the ring (in the case when the solid-body field and the ring initially co-rotate) or extract energy from the ring (when the solid-body field and the ring initially counter-rotate), hence the Hamiltonian and the centre-of-vorticity vector associated with the N -point vortices are no longer conserved as they are for the one-way coupled model described by Newton & Shokraneh. In the first case, energy is transferred to the ring, the length of the centre-of-vorticity vector increases, while its tip spirals in a clockwise manner towards the North Pole. The ring stays relatively intact for short times, but ultimately breaks-up on a longer time-scale. In the latter case, energy is extracted from the ring, the length of the centre-of-vorticity vector decreases while its tip spirals towards the North Pole and the ring loses its coherence more quickly than in the co-rotating case. The special case where the ring is initially oriented so that its centre-of-vorticity vector is perpendicular to the axis of rotation is also examined as it shows how the coupling to the background field breaks this symmetry. In ... |
format |
Article in Journal/Newspaper |
author |
Newton, Paul K Sakajo, Takashi |
spellingShingle |
Newton, Paul K Sakajo, Takashi The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field |
author_facet |
Newton, Paul K Sakajo, Takashi |
author_sort |
Newton, Paul K |
title |
The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field |
title_short |
The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field |
title_full |
The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field |
title_fullStr |
The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field |
title_full_unstemmed |
The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field |
title_sort |
n -vortex problem on a rotating sphere. iii. ring configurations coupled to a background field |
publisher |
The Royal Society |
publishDate |
2007 |
url |
http://dx.doi.org/10.1098/rspa.2006.1802 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2006.1802 https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2006.1802 |
geographic |
North Pole |
geographic_facet |
North Pole |
genre |
North Pole |
genre_facet |
North Pole |
op_source |
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 463, issue 2080, page 961-977 ISSN 1364-5021 1471-2946 |
op_rights |
https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ |
op_doi |
https://doi.org/10.1098/rspa.2006.1802 |
container_title |
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
container_volume |
463 |
container_issue |
2080 |
container_start_page |
961 |
op_container_end_page |
977 |
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1800758124435472384 |