The Gulf Stream shows a large meander off Cape Hatteras. This is driven by an energy conversion process known as baroclinic instability and observations suggest that nonlinearity is an important part in this process. In order to understand the fundamental role of nonlinearity in baroclinic instability, an inviscid 2-layer quasi-geostrophic model is studied.
The linear solution is obtained by methods of normal mode and Fourier-Laplace transforms. It is found that the set corresponding to the continuous spectrum is null and the set corresponding to the discrete spectrum is complete.
The nonlinear solution is expanded in terms of the complete set of the eigenfunctions in the north-south direction and a Fourier series in the east-west direction. Using a certain form of orthogonality of the eigenfunctions, a 6-dimensional dynamical system which solves for the amplitudes of the components is derived. A solution to this system is obtained for certain initial conditions using the Runge-Kutta method. In particular, it is found that stability of any solution of this system, such as a fixed point x = 0, can be determined by transforming the system into a set of Hamiltonian equations.
A computed meander represents either an eastward or a westward propagating wave with an amplitude vacillation. Effects of severe truncation appear to be significant in some cases. Judging from the solution of the dynamical system, the computed meander is found to be quasi-periodic and sensitive to initial conditions.
","abstract_html":"<p>The Gulf Stream shows a large meander off Cape Hatteras. This is driven by an energy conversion process known as baroclinic instability and observations suggest that nonlinearity is an important part in this process. In order to understand the fundamental role of nonlinearity in baroclinic instability, an inviscid 2-layer quasi-geostrophic model is studied.</p> <p>The linear solution is obtained by methods of normal mode and Fourier-Laplace transforms. It is found that the set corresponding to the continuous spectrum is null and the set corresponding to the discrete spectrum is complete.</p> <p>The nonlinear solution is expanded in terms of the complete set of the eigenfunctions in the north-south direction and a Fourier series in the east-west direction. Using a certain form of orthogonality of the eigenfunctions, a 6-dimensional dynamical system which solves for the amplitudes of the components is derived. A solution to this system is obtained for certain initial conditions using the Runge-Kutta method. In particular, it is found that stability of any solution of this system, such as a fixed point x = 0, can be determined by transforming the system into a set of Hamiltonian equations.</p> <p>A computed meander represents either an eastward or a westward propagating wave with an amplitude vacillation. Effects of severe truncation appear to be significant in some cases. Judging from the solution of the dynamical system, the computed meander is found to be quasi-periodic and sensitive to initial conditions.</p>","abstract_has_math":false,"creators":["Oka, Eiichi"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Ocean & Earth Sciences","degree_department":null,"school":null,"contributors":["Chester E. Grosch","Gabriel T. Csanady","Ronald E. Johnson","John A. Adam"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989-10-01T07:00:00Z","date_published":"1989-10-01T07:00:00Z","updated_at":"2026-07-24T03:35:30Z","subjects":["Baroclinicity","Baroclinic models","Gulf Stream","Oceanography"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.odu.edu/oeas_etds/150","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chester E. Grosch","Gabriel T. Csanady","Ronald E. Johnson","John A. Adam"]},{"key":"dc:creator","label":"Author","values":["Oka, Eiichi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-23T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Ocean & Earth Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Baroclinicity","Baroclinic models","Gulf Stream","Oceanography"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.odu.edu/oeas_etds/150"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Gulf Stream shows a large meander off Cape Hatteras. This is driven by an energy conversion process known as baroclinic instability and observations suggest that nonlinearity is an important part in this process. In order to understand the fundamental role of nonlinearity in baroclinic instability, an inviscid 2-layer quasi-geostrophic model is studied.
The linear solution is obtained by methods of normal mode and Fourier-Laplace transforms. It is found that the set corresponding to the continuous spectrum is null and the set corresponding to the discrete spectrum is complete.
The nonlinear solution is expanded in terms of the complete set of the eigenfunctions in the north-south direction and a Fourier series in the east-west direction. Using a certain form of orthogonality of the eigenfunctions, a 6-dimensional dynamical system which solves for the amplitudes of the components is derived. A solution to this system is obtained for certain initial conditions using the Runge-Kutta method. In particular, it is found that stability of any solution of this system, such as a fixed point x = 0, can be determined by transforming the system into a set of Hamiltonian equations.
A computed meander represents either an eastward or a westward propagating wave with an amplitude vacillation. Effects of severe truncation appear to be significant in some cases. Judging from the solution of the dynamical system, the computed meander is found to be quasi-periodic and sensitive to initial conditions.
"]},{"key":"dc:title","label":"Title","values":["Nonlinear Solutions to a Two-Layer Quasi-Geostrophic Model of the Gulf Stream"]}]}],"canonical_facts":{"dc:contributor":["Chester E. Grosch","Gabriel T. Csanady","Ronald E. Johnson","John A. Adam"],"dc:creator":["Oka, Eiichi"],"dc:date.available":["2019-10-23T07:00:00Z"],"dc:description.abstract":["The Gulf Stream shows a large meander off Cape Hatteras. This is driven by an energy conversion process known as baroclinic instability and observations suggest that nonlinearity is an important part in this process. In order to understand the fundamental role of nonlinearity in baroclinic instability, an inviscid 2-layer quasi-geostrophic model is studied.
The linear solution is obtained by methods of normal mode and Fourier-Laplace transforms. It is found that the set corresponding to the continuous spectrum is null and the set corresponding to the discrete spectrum is complete.
The nonlinear solution is expanded in terms of the complete set of the eigenfunctions in the north-south direction and a Fourier series in the east-west direction. Using a certain form of orthogonality of the eigenfunctions, a 6-dimensional dynamical system which solves for the amplitudes of the components is derived. A solution to this system is obtained for certain initial conditions using the Runge-Kutta method. In particular, it is found that stability of any solution of this system, such as a fixed point x = 0, can be determined by transforming the system into a set of Hamiltonian equations.
A computed meander represents either an eastward or a westward propagating wave with an amplitude vacillation. Effects of severe truncation appear to be significant in some cases. Judging from the solution of the dynamical system, the computed meander is found to be quasi-periodic and sensitive to initial conditions.
"],"dc:identifier":["https://digitalcommons.odu.edu/oeas_etds/150"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Baroclinicity","Baroclinic models","Gulf Stream","Oceanography"],"dc:title":["Nonlinear Solutions to a Two-Layer Quasi-Geostrophic Model of the Gulf Stream"],"thesis:degree_discipline":["Ocean & Earth Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:30Z"}