Characterization of instabilities in the problem of elastic planetary tides

Persistent Link:
http://hdl.handle.net/10150/280697
Title:
Characterization of instabilities in the problem of elastic planetary tides
Author:
Frey, Sarah E.
Issue Date:
2004
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:
In 1911, A. E. H. Love published a linear elastic model for the tidal deformation of planetary bodies. Using numerical techniques that were unavailable to Love, surprising behaviors of the tidal solution have been found: tides of finite, even substantial, height are possible in the presence of an infinitesimal tide raiser, thus indicating some sort of instability. The Love tidal model was for the deformation of a homogeneous sphere. In order to better understand the nature of the instabilities in this model, I consider the effect of adding a radially dependent density profile to the model. For a given singularity, an increase in the initial density gradient causes the singularity to change locations in parameter space. For steep enough density gradient, the singularity is pushed outside the realm of physically meaningful parameter space for certain initial radial density profiles. Self-gravitation appears to be the likely mechanism for the driving of the tidal instability. The nature of the behavior of self-gravitation will be studied by considering an exact elastic formulation of the problem. In this way, a more complete view of the processes involved in the tidal deformation of a body can be explored. I find that each of the curves of singularity loci observed in the tidal problem correspond to instabilities in different modes for the exact elastic self-gravitation problem.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Geodesy.; Geophysics.; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Greenberg, Richard; Tabor, Michael

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleCharacterization of instabilities in the problem of elastic planetary tidesen_US
dc.creatorFrey, Sarah E.en_US
dc.contributor.authorFrey, Sarah E.en_US
dc.date.issued2004en_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.abstractIn 1911, A. E. H. Love published a linear elastic model for the tidal deformation of planetary bodies. Using numerical techniques that were unavailable to Love, surprising behaviors of the tidal solution have been found: tides of finite, even substantial, height are possible in the presence of an infinitesimal tide raiser, thus indicating some sort of instability. The Love tidal model was for the deformation of a homogeneous sphere. In order to better understand the nature of the instabilities in this model, I consider the effect of adding a radially dependent density profile to the model. For a given singularity, an increase in the initial density gradient causes the singularity to change locations in parameter space. For steep enough density gradient, the singularity is pushed outside the realm of physically meaningful parameter space for certain initial radial density profiles. Self-gravitation appears to be the likely mechanism for the driving of the tidal instability. The nature of the behavior of self-gravitation will be studied by considering an exact elastic formulation of the problem. In this way, a more complete view of the processes involved in the tidal deformation of a body can be explored. I find that each of the curves of singularity loci observed in the tidal problem correspond to instabilities in different modes for the exact elastic self-gravitation problem.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectGeodesy.en_US
dc.subjectGeophysics.en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGreenberg, Richarden_US
dc.contributor.advisorTabor, Michaelen_US
dc.identifier.proquest3158092en_US
dc.identifier.bibrecord.b48126986en_US
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