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The Dynamics of a Three-Dimensional ...

Sivakumar, Adhithiya.

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The Dynamics of a Three-Dimensional Heton.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Dynamics of a Three-Dimensional Heton./
Author:	Sivakumar, Adhithiya.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	56 p.
Notes:	Source: Masters Abstracts International, Volume: 81-03.
Contained By:	Masters Abstracts International81-03.
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13860775
ISBN:	9781085624688

The Dynamics of a Three-Dimensional Heton.
Sivakumar, Adhithiya.

The Dynamics of a Three-Dimensional Heton. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 56 p.

Source: Masters Abstracts International, Volume: 81-03.

Thesis (M.S.)--University of Colorado at Boulder, 2019.

This item must not be sold to any third party vendors.

Hetons are defined, in two-layer quasigeostrophy, as tilted counter-rotating baroclinic vortex pairs with each vortex present in a different layer. The study of hetons is motivated by their usage within the context of two-layer quasigeostrophic theory to model the transport of heat in a number of geophysical flows including, perhaps most famously, advection in the open ocean. A number of variations and generalizations of the heton concept exist in literature. Here, following the work of V.M. Gryanik, we investigate the three-dimensional point vortex heton. We start with the derivation of a non-canonical Hamiltonian system of 2n ODEs corresponding to point vortex solutions of the Quasigeostrophic Potential Vorticity Equation in an unbounded three-dimensional domain, where n is the number of point vortices. We then show that three-dimensional hetons arise naturally as solutions of this system when n = 2. The dynamics of a single three-dimensional heton in a comoving frame are then discussed. Fixed points and bifurcations in the Lagrangian trajectories are then catalogued using various analytical and numerical techniques, and finally, the volume trapped by a single three-dimensional heton is calculated numerically for various values of the parameter Z - corresponding to the vertical distance between the counter-rotating vortices that compose the heton.

ISBN: 9781085624688Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Dynamical Systems

The Dynamics of a Three-Dimensional Heton.
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245 1 4 $a The Dynamics of a Three-Dimensional Heton.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 56 p.
500 $a Source: Masters Abstracts International, Volume: 81-03.
500 $a Advisor: Weiss, Jeffrey.
502 $a Thesis (M.S.)--University of Colorado at Boulder, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Hetons are defined, in two-layer quasigeostrophy, as tilted counter-rotating baroclinic vortex pairs with each vortex present in a different layer. The study of hetons is motivated by their usage within the context of two-layer quasigeostrophic theory to model the transport of heat in a number of geophysical flows including, perhaps most famously, advection in the open ocean. A number of variations and generalizations of the heton concept exist in literature. Here, following the work of V.M. Gryanik, we investigate the three-dimensional point vortex heton. We start with the derivation of a non-canonical Hamiltonian system of 2n ODEs corresponding to point vortex solutions of the Quasigeostrophic Potential Vorticity Equation in an unbounded three-dimensional domain, where n is the number of point vortices. We then show that three-dimensional hetons arise naturally as solutions of this system when n = 2. The dynamics of a single three-dimensional heton in a comoving frame are then discussed. Fixed points and bifurcations in the Lagrangian trajectories are then catalogued using various analytical and numerical techniques, and finally, the volume trapped by a single three-dimensional heton is calculated numerically for various values of the parameter Z - corresponding to the vertical distance between the counter-rotating vortices that compose the heton.
590 $a School code: 0051.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Atmospheric sciences. $3 3168354
653 $a Dynamical Systems
653 $a Heton
653 $a Point vortex
653 $a Quasigeostrophic Theory
690 $a 0364
690 $a 0725
710 2 $a University of Colorado at Boulder. $b Applied Mathematics. $3 1030307
773 0 $t Masters Abstracts International $g 81-03.
790 $a 0051
791 $a M.S.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13860775