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Volume Transport by a 3D Quasigeostrophic Heton

by 1,*,† and 2,*,†
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, CO 80309, USA
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Xavier Carton and Sabrina Speich
Fluids 2022, 7(3), 92;
Received: 16 January 2022 / Revised: 22 February 2022 / Accepted: 28 February 2022 / Published: 2 March 2022
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
Oceanic flows self-organize into coherent vortices, which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal circulations. Here, we investigate the structure of the transport induced by a single three-dimensional heton. The transport is determined by the Hamiltonian structure of the velocity field induced by the heton’s component vortices. The dynamics display a sequence of bifurcations as one moves through the heton-induced velocity field in height. These bifurcations create and destroy unstable fixed points whose associated invariant manifolds bound the trapped volume. Heton configurations fall into three categories. Vertically aligned hetons, which are parallel to the vertical axis and have zero horizontal separation, do not move and do not transport fluid. Horizontally aligned hetons, which lie on the horizontal plane and have zero vertical separation, have a single parameter, the horizontal vortex half-separation Y, and simple scaling shows the dimensional trapped volume scales as Y3. Tilted hetons are described by two parameters, Y and the vertical vortex half-separation Z, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as Z4/Y for large Z. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory. View Full-Text
Keywords: heton; quasigeostrophic; point vortex heton; quasigeostrophic; point vortex
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MDPI and ACS Style

Sivakumar, A.; Weiss, J.B. Volume Transport by a 3D Quasigeostrophic Heton. Fluids 2022, 7, 92.

AMA Style

Sivakumar A, Weiss JB. Volume Transport by a 3D Quasigeostrophic Heton. Fluids. 2022; 7(3):92.

Chicago/Turabian Style

Sivakumar, Adhithiya, and Jeffrey B. Weiss. 2022. "Volume Transport by a 3D Quasigeostrophic Heton" Fluids 7, no. 3: 92.

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