NUMERICAL STUDIES OF BAROCLINIC INSTABILITY IN CYLINDRICAL AND SPHERICAL DOMAINS.

Persistent Link:
http://hdl.handle.net/10150/184237
Title:
NUMERICAL STUDIES OF BAROCLINIC INSTABILITY IN CYLINDRICAL AND SPHERICAL DOMAINS.
Author:
MILLER, TIMOTHY LEE.
Issue Date:
1982
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Finite difference numerical models based upon the Navier-Stokes equations with the Boussinesq approximation have been utilized to study the dynamics of a rotating liquid with horizontal density gradients. There are two configurations analyzed: a cylindrical annulus of water rotating about a vertical axis (parallel to the body force), and a hemispherical shell of silicone oil with a radial body force, rotating about the polar axis. In both the cylindrical and spherical configurations, the thermal and mechanical forcings (boundary conditions) are symmetric about the axis of rotation. The physical parameters varied are the rotation rate and the amplitude of the horizontal thermal forcing. Two numerical models have been developed for each geometrical configuration: one to calculate axisymmetric flows and another to test the stability of those flows to non-axisymmetric perturbations. The primary purpose of the models is to determine whether axisymmetric or non-axisymmetric flow will be observed in a corresponding laboratory experiment. For the cylindrical annulus, the predictions of axisymmetric and non-axisymmetric flow are in good agreement with laboratory experiments previously performed. In the spherical experiment considered, which has not been performed in the laboratory, there is evidence that if the rotation rate is fixed and the latitudinal thermal forcing is reduced, there exists a transition from non-axisymmetric to axisymmetric flow, but that as the rotation rate is decreased for a fixed latitudinal thermal gradient on the boundaries, the flow does not become axisymmetric. The structures of some of the fastest growing eigenmodes are presented for both cylindrical and spherical cases. Analyses of the energetics indicate that the waves in all cases considered are essentially baroclinic in nature.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Atmospheric circulation -- Mathematical models.; Baroclinic models.; Dynamic meteorology -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Gall, Robert

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNUMERICAL STUDIES OF BAROCLINIC INSTABILITY IN CYLINDRICAL AND SPHERICAL DOMAINS.en_US
dc.creatorMILLER, TIMOTHY LEE.en_US
dc.contributor.authorMILLER, TIMOTHY LEE.en_US
dc.date.issued1982en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractFinite difference numerical models based upon the Navier-Stokes equations with the Boussinesq approximation have been utilized to study the dynamics of a rotating liquid with horizontal density gradients. There are two configurations analyzed: a cylindrical annulus of water rotating about a vertical axis (parallel to the body force), and a hemispherical shell of silicone oil with a radial body force, rotating about the polar axis. In both the cylindrical and spherical configurations, the thermal and mechanical forcings (boundary conditions) are symmetric about the axis of rotation. The physical parameters varied are the rotation rate and the amplitude of the horizontal thermal forcing. Two numerical models have been developed for each geometrical configuration: one to calculate axisymmetric flows and another to test the stability of those flows to non-axisymmetric perturbations. The primary purpose of the models is to determine whether axisymmetric or non-axisymmetric flow will be observed in a corresponding laboratory experiment. For the cylindrical annulus, the predictions of axisymmetric and non-axisymmetric flow are in good agreement with laboratory experiments previously performed. In the spherical experiment considered, which has not been performed in the laboratory, there is evidence that if the rotation rate is fixed and the latitudinal thermal forcing is reduced, there exists a transition from non-axisymmetric to axisymmetric flow, but that as the rotation rate is decreased for a fixed latitudinal thermal gradient on the boundaries, the flow does not become axisymmetric. The structures of some of the fastest growing eigenmodes are presented for both cylindrical and spherical cases. Analyses of the energetics indicate that the waves in all cases considered are essentially baroclinic in nature.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectAtmospheric circulation -- Mathematical models.en_US
dc.subjectBaroclinic models.en_US
dc.subjectDynamic meteorology -- Mathematical models.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGall, Roberten_US
dc.identifier.proquest8223011en_US
dc.identifier.oclc682913372en_US
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