The role of the complete Coriolis force in cross-equatorial transport of abyssal ocean currents
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| Title: | The role of the complete Coriolis force in cross-equatorial transport of abyssal ocean currents |
|---|---|
| Authors: | Stewart, Andrew L. |
| Committee Members: | Dellar, Paul J. |
| Summary: | In studies of the ocean it has become conventional to retain only the component of the Coriolis force associated with the radial component of the Earth’s rotation vector, the so-called “traditional approximation”. We investigate the role of the “non-traditional” component of the Coriolis force, corresponding to the non-radial component of the rotation vector, in transporting abyssal waters across the equator. We first derive a non-traditional generalisation of the multi-layer shallow water equations, which describe the flow of multiple superposed layers of inviscid, incompressible fluid with constant densities over prescribed topography in a rotating frame. We derive these equations both by averaging the three-dimensional governing equations over each layer, and via Hamilton’s principle. The latter derivation guarantees that conservation laws for mass, momentum, energy and potential vorticity are preserved. Within geophysically realistic parameters, including the complete Coriolis force modifies the domain of hyperbolicity of the multi-layer equations by no more than 5%. By contrast, long linear plane waves exhibit dramatic structural changes due to reconnection of the surface and internal wave modes in the long-wave limit. We use our non-traditional shallow water equations as an idealised model of an abyssal current flowing beneath a less dense upper ocean. We focus on the Antarctic Bottom Water, which crosses the equator in the western Atlantic ocean, where the bathymetry forms an almost-westward channel. Cross-equatorial flow is strongly constrained by potential vorticity conservation, which requires fluid to acquire a large relative vorticity in order to move between hemispheres. Including the complete Coriolis force accounts for the fact that fluid crossing the equator in an eastward/westward channel experiences a smaller change in angular momentum, and therefore acquires less relative vorticity. Our analytical and numerical solutions for shallow water flow over idealised channel topography show that the non-traditional component of the Coriolis force facilitates cross-equatorial flow through an almost-westward channel. |
| URL: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547493 |
| Database: | OpenDissertations |
| FullText | Text: Availability: 0 |
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| Header | DbId: ddu DbLabel: OpenDissertations An: ddu.oai.ethos.bl.uk.547493 AccessLevel: 6 PubType: Dissertation/ Thesis PubTypeId: dissertation PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The role of the complete Coriolis force in cross-equatorial transport of abyssal ocean currents – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Stewart%2C+Andrew+L%2E%22">Stewart, Andrew L.</searchLink> – Name: Author Label: Committee Members Group: Au Data: <searchLink fieldCode="CO" term="%22Dellar%2C+Paul+J%2E%22">Dellar, Paul J.</searchLink> – Name: Abstract Label: Summary Group: Ab Data: In studies of the ocean it has become conventional to retain only the component of the Coriolis force associated with the radial component of the Earth’s rotation vector, the so-called “traditional approximation”. We investigate the role of the “non-traditional” component of the Coriolis force, corresponding to the non-radial component of the rotation vector, in transporting abyssal waters across the equator. We first derive a non-traditional generalisation of the multi-layer shallow water equations, which describe the flow of multiple superposed layers of inviscid, incompressible fluid with constant densities over prescribed topography in a rotating frame. We derive these equations both by averaging the three-dimensional governing equations over each layer, and via Hamilton’s principle. The latter derivation guarantees that conservation laws for mass, momentum, energy and potential vorticity are preserved. Within geophysically realistic parameters, including the complete Coriolis force modifies the domain of hyperbolicity of the multi-layer equations by no more than 5%. By contrast, long linear plane waves exhibit dramatic structural changes due to reconnection of the surface and internal wave modes in the long-wave limit. We use our non-traditional shallow water equations as an idealised model of an abyssal current flowing beneath a less dense upper ocean. We focus on the Antarctic Bottom Water, which crosses the equator in the western Atlantic ocean, where the bathymetry forms an almost-westward channel. Cross-equatorial flow is strongly constrained by potential vorticity conservation, which requires fluid to acquire a large relative vorticity in order to move between hemispheres. Including the complete Coriolis force accounts for the fact that fluid crossing the equator in an eastward/westward channel experiences a smaller change in angular momentum, and therefore acquires less relative vorticity. Our analytical and numerical solutions for shallow water flow over idealised channel topography show that the non-traditional component of the Coriolis force facilitates cross-equatorial flow through an almost-westward channel. – Name: URL Label: URL Group: URL Data: <link linkTarget="URL" linkTerm="https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547493" linkWindow="_blank">https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547493</link> |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English Subjects: – SubjectFull: 551.46 Type: general – SubjectFull: Mathematics ; Approximations and expansions ; Fluid mechanics (mathematics) ; Geophysics (mathematics) ; geophysical fluid dynamics ; computational applied mathematics ; Hamiltonian mechanics ; asymptotic analysis ; complete Coriolis force ; ocean currents ; cross-equatorial flow ; shallow water equations Type: general Titles: – TitleFull: The role of the complete Coriolis force in cross-equatorial transport of abyssal ocean currents Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Stewart, Andrew L. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2011 |
| ResultId | 1 |
