Abstract/Details

Characterization of instabilities in the problem of elastic planetary tides


2004 2004

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Abstract (summary)

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.

Indexing (details)


Subject
Mathematics;
Earth;
Geophysics
Classification
0405: Mathematics
0370: Earth
0373: Geophysics
Identifier / keyword
Pure sciences; Earth sciences; Elastic planetary tides; Love number
Title
Characterization of instabilities in the problem of elastic planetary tides
Author
Frey, Sarah E.
Number of pages
115
Publication year
2004
Degree date
2004
School code
0009
Source
DAI-B 65/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780496905645, 0496905643
Advisor
Greenberg, Richard; Tabor, Michael
University/institution
The University of Arizona
University location
United States -- Arizona
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3158092
ProQuest document ID
305208278
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305208278/fulltextPDF
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