dorsal/arxiv
View SchemaDNS of bifurcations in an air-filled rotating baroclinic annulus
| Authors | Anthony Randriamampianina, Wolf-Gerrit Fruh, Peter L. Read, Pierre Maubert |
|---|---|
| Categories | |
| ArXiv ID | physics/0607157 |
| URL | https://arxiv.org/abs/physics/0607157 |
| DOI | 10.1017/S0022112006000711 |
| Journal | Journal of Fluid Mechanics a venir (2006) a venir |
Abstract
Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating is presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies by Maubert and Randriamampianina, the fluid used is air rather than a liquid as used in all other previous work. This study investigated a bifurcation sequence from the axisymmetric flow to a number of complex flows. The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady, fully-developed baroclinic wave to chaotic flow followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic MAV\@. In the context of the baroclinic annulus this sequence is unusual as the vacillation is usually found on decrease of the rotation rate from the steady wave flow. Further transitions of a steady wave with a higher wave number pointed to the possibility that a barotropic instability of the side wall boundary layers and the subsequent breakdown of these barotropic vortices may play a role in the transition to structural vacillation and, ultimately, geostrophic turbulence.
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"abstract": "Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics\nand a route to chaos in a rotating fluid subjected to lateral heating is\npresented here and discussed in the context of laboratory experiments in the\nbaroclinic annulus. Following two previous preliminary studies by Maubert and\nRandriamampianina, the fluid used is air rather than a liquid as used in all\nother previous work. This study investigated a bifurcation sequence from the\naxisymmetric flow to a number of complex flows. The transition sequence, on\nincrease of the rotation rate, from the axisymmetric solution via a steady,\nfully-developed baroclinic wave to chaotic flow followed a variant of the\nclassical quasi-periodic bifurcation route, starting with a subcritical Hopf\nand associated saddle-node bifurcation. This was followed by a sequence of two\nsupercritical Hopf-type bifurcations, first to an amplitude vacillation, then\nto a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and\nfinally to a chaotic MAV\\@. In the context of the baroclinic annulus this\nsequence is unusual as the vacillation is usually found on decrease of the\nrotation rate from the steady wave flow. Further transitions of a steady wave\nwith a higher wave number pointed to the possibility that a barotropic\ninstability of the side wall boundary layers and the subsequent breakdown of\nthese barotropic vortices may play a role in the transition to structural\nvacillation and, ultimately, geostrophic turbulence.",
"arxiv_id": "physics/0607157",
"authors": [
"Anthony Randriamampianina",
"Wolf-Gerrit Fruh",
"Peter L. Read",
"Pierre Maubert"
],
"categories": [
"physics.geo-ph",
"physics.class-ph"
],
"doi": "10.1017/S0022112006000711",
"journal_ref": "Journal of Fluid Mechanics a venir (2006) a venir",
"title": "DNS of bifurcations in an air-filled rotating baroclinic annulus",
"url": "https://arxiv.org/abs/physics/0607157"
},
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