Numerical solutions of the inertial modes of the earth's fluid core : from the outstanding problem of the incompressible fluid shell to more realistic up to date core models

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dc.contributor.authorNaseri, Hossein
dc.contributor.supervisorSeyed-Mahmoud, Behnam
dc.date.accessioned2015-05-05T21:49:03Z
dc.date.available2015-05-05T21:49:03Z
dc.date.issued2015
dc.degree.levelMastersen_US
dc.description.abstractIn this work we study the inertial modes of a rotating spheroidal fluid shell proportional to the Earth's fluid core. We start with the long standing problem of the modes of an incompressible and inviscid spherical fluid shell. Traditionally, a second order equation describing the pressure field of the flow, subject to the impermeability boundary condition, is solved for the eigenfrequencies and eigenfunctions of the flow. These equations are scalar hyperbolic boundary value second-order Partial Differential Equations (PDEs) which are ill-posed problems in the sense that the existence of the analytical solutions depends on the geometry of the container. The problem admits analytical solutions in a sphere but not in a spherical shell. We use the Galekin method to solve the momentum and the continuity equation together and compute the frequencies, pressure and displacement eigenfunctions for some of the low order, wavenumbers $m=0$ and $m=1$, inertial modes of this model. To show that our approach is correct we compute the inertial modes of a homogeneous, incompressible and inviscid fluid sphere for which analytical solutions for the inertial modes exist. We also compute the inertial modes of a more realistic uniformly rotating, compressible, self gravitation and inviscid fluid core model. Finally, we extend the governing equations to include first order terms in the ellipticity. In order to minimize effects of the derivatives of the material properties which are poorly determined in the existing Earth models, a Clairaut coordinate system is used to map the elliptical equipotential surfaces into the spherical ones. Also, the divergence theorem is used to implement the boundary equations.en_US
dc.description.sponsorshipNatural Sciences and Engineering Research Council (NSERC) of Canada , School of Graduate Studies (SGS)en_US
dc.embargoNoen_US
dc.identifier.urihttps://hdl.handle.net/10133/3678
dc.language.isoen_CAen_US
dc.proquest.subject0373en_US
dc.proquest.subject0596en_US
dc.proquest.subject0605en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Physics and Astronomyen_US
dc.publisher.departmentDepartment of Physics and Astronomyen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectearth's coreen_US
dc.subjectrotating fluidsen_US
dc.subjectinertial modesen_US
dc.subjecthydrostatic equilibriumen_US
dc.subjectGalerkin methoden_US
dc.subjectcompressibilityen_US
dc.subjectelastic boundary conditionsen_US
dc.subjectellipsoidal coreen_US
dc.subjectClairaut coordinatesen_US
dc.titleNumerical solutions of the inertial modes of the earth's fluid core : from the outstanding problem of the incompressible fluid shell to more realistic up to date core modelsen_US
dc.typeThesisen_US
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