Elliptical instability in the planetary fluid cores
University of Lethbridge. Faculty of Arts and Science
Lethbridge, Alta. : University of Lethbridge, Dept. of Physics and Astronomy, 2014
Elliptical instability may be excited in any rotating flow with elliptically deformed streamlines. Investigating this instability in containers with spheroidal or ellipsoidal boundaries is of geophysical and astrophysical interest as many stars and planets are either rotating ellipsoidal fluid bodies or have substantial fluid cores which are either ellipsoidal, in the absence of a solid inner core, or ellipsoidal shells such as the Earth’s fluid core; elliptical instability may be excited in these bodies as a result of the gravitational pull of a secondary body such as a moon or a large asteroid orbiting these bodies. In this thesis, the nonlinear evolution of elliptical instability in an inviscid incompressible rotating triaxial ellipsoid is numerically studied using the least-square finite element method. After validating the method by reproducing some known results, it is applied to other configurations in order to investigate some open questions on this subject, namely, the effects of the oblateness of the ellipsoid and the frequency ratio of the orbital speed of the secondary body on the evolution of the elliptical instability. We have found that if the parameters of the system, i.e. the flattening ratio and the frequency ratio of the background rotation, are in the range of the spin-over instability, a repetitive three-dimensional rigorous motion is maintained indefinitely; otherwise, instability may be excited initially, once the streamlines become elliptical, for certain ranges of the system parameters; however, as time elapses the motion becomes two dimensional with small displacement amplitudes in x- and y- directions.
x, 111 leaves ; 29 cm
Elliptical instability , Parallel computing , OpenMP , Least-square finite element method , Fluid cores , Dissertations, Academic , Attractions of ellipsoids , Rotating masses of fluids