Volume Transport by a 3D Quasigeostrophic Heton
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/3/92 |
| _version_ | 1797471688488648704 |
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| author | Adhithiya Sivakumar Jeffrey B. Weiss |
| author_facet | Adhithiya Sivakumar Jeffrey B. Weiss |
| author_sort | Adhithiya Sivakumar |
| collection | DOAJ |
| description | 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 <i>Y</i>, and simple scaling shows the dimensional trapped volume scales as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Y</mi><mn>3</mn></msup></semantics></math></inline-formula>. Tilted hetons are described by two parameters, <i>Y</i> and the vertical vortex half-separation <i>Z</i>, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>Z</mi><mn>4</mn></msup><mo>/</mo><mi>Y</mi></mrow></semantics></math></inline-formula> for large <i>Z</i>. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory. |
| first_indexed | 2024-03-09T19:51:44Z |
| format | Article |
| id | doaj.art-ef143c641ba14fccacad4f4b26c1510c |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T19:51:44Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-ef143c641ba14fccacad4f4b26c1510c2023-11-24T01:09:15ZengMDPI AGFluids2311-55212022-03-01739210.3390/fluids7030092Volume Transport by a 3D Quasigeostrophic HetonAdhithiya Sivakumar0Jeffrey B. Weiss1Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USADepartment of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, CO 80309, USAOceanic 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 <i>Y</i>, and simple scaling shows the dimensional trapped volume scales as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Y</mi><mn>3</mn></msup></semantics></math></inline-formula>. Tilted hetons are described by two parameters, <i>Y</i> and the vertical vortex half-separation <i>Z</i>, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>Z</mi><mn>4</mn></msup><mo>/</mo><mi>Y</mi></mrow></semantics></math></inline-formula> for large <i>Z</i>. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory.https://www.mdpi.com/2311-5521/7/3/92hetonquasigeostrophicpoint vortex |
| spellingShingle | Adhithiya Sivakumar Jeffrey B. Weiss Volume Transport by a 3D Quasigeostrophic Heton Fluids heton quasigeostrophic point vortex |
| title | Volume Transport by a 3D Quasigeostrophic Heton |
| title_full | Volume Transport by a 3D Quasigeostrophic Heton |
| title_fullStr | Volume Transport by a 3D Quasigeostrophic Heton |
| title_full_unstemmed | Volume Transport by a 3D Quasigeostrophic Heton |
| title_short | Volume Transport by a 3D Quasigeostrophic Heton |
| title_sort | volume transport by a 3d quasigeostrophic heton |
| topic | heton quasigeostrophic point vortex |
| url | https://www.mdpi.com/2311-5521/7/3/92 |
| work_keys_str_mv | AT adhithiyasivakumar volumetransportbya3dquasigeostrophicheton AT jeffreybweiss volumetransportbya3dquasigeostrophicheton |