Elliptical Instabilities of Stratified, Hydromagnetic Waves and the Earth's Outer Core.
The streamlines of the basic rotating flow within the Earth's outer core are thought to be slightly elliptical due to tidal and precessional effects. This distortion has been implicitly assumed unimportant in past analyses of the core. However recently, it has been realised that such a 2-dimensional elliptical flow is inertially unstable to 3-dimensional disturbances. This thesis assesses the relevance of this elliptical instability for the Earth's outer core and discusses possible implications for the geodynamo. Elliptical instability arises through a triad -type resonance of two linear waves with the underlying distorted state. When the fluid is stratified and carries a magnetic field, three different sets of waves, categorised by their dominant restoring mechanism, can exist and may potentially excite each other through the elliptical distortion. Simple cylindrical models are constructed to examine these various couplings using Earth-like parameters. In particular, it is estimated that resonances between fast (frequency comparable to the basic rotation) hydromagnetic waves can produce growth with an e-folding time of 100,000 years in the outer core, comparing favourably with typical geomagnetic inter-reversal times of O(10^5/10^6) years. Extension is made to the more geophysically-relevant, elliptically-distorted spheroidal container, in which, regardless of the oblateness, an upper bound of 9/16 beta is deduced for the exponential growth rate (beta is the ratio of strain to rotation rate for the elliptical flow). Results indicate that the breakdown of a slightly distorted, rotating spheroid through an elliptical instability is commonplace. The effect of an orbiting moon is discussed and connection made between the well-known "middle-moment-of-inertia" instability of rotating, rigid bodies and the elliptical instability. To assess the effect of ohmic and viscous dissipations upon these instabilities, a boundary layer analysis is undertaken to calculate hydromagnetic decay rates for the relevant fast waves in the outer core. It is found that the elliptical excitation of these fast hydromagnetic waves is just insufficient to overcome dissipative processes within the modeling assumptions made concerning the core -mantle boundary. The closeness in size of these competing effects is striking and may not be coincidental. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
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- Mathematics; Physics: Fluid and Plasma; Geophysics