Hydromagnetic waves in Earth's core and their influence on ...

iAbstractIn this thesis east-west motions of Earth’s magnetic field on time scales of centuriesto millennia <strong>and</strong> associated patterns of field evolution at the <strong>core</strong> surface are studied.The hypothesis that hydromagnetic <strong>waves</strong> <strong>in</strong> Earth’s <strong>core</strong> contribute to such changes is<strong>in</strong>vestigated by compar<strong>in</strong>g analysis of historical <strong>and</strong> archeomagnetic observations withpredictions from analytical <strong>and</strong> numerical wave models.Geomagnetic field models are analysed <strong>in</strong> order to quantify the characteristics of radialmagnetic field (B r ) evolution at the <strong>core</strong> surface. In the historical model gufm1, spatially<strong>and</strong> temporally coherent (wave-like) patterns are identified <strong>in</strong> B r . Particularly strik<strong>in</strong>gis a low latitude signal with azimuthal wavenumber m=5 that travels westwards at∼17 km yr −1 . Study<strong>in</strong>g the archeomagnetic model CALS7K.1, episodes of both eastward<strong>and</strong> westward motion of wave-like patterns <strong>in</strong> B r are observed. Analysis of the evolutionof fields <strong>and</strong> underly<strong>in</strong>g flows from geodynamo simulations is used to illustrate that<strong>in</strong>ability to resolve the smallest length scales of the field makes quantitative <strong>in</strong>ferencesconcern<strong>in</strong>g the flow difficult, unless the flow is large scale. Furthermore, it is foundazimuthal motions of patterns <strong>in</strong> B r can be produced by hydromagnetic <strong>waves</strong> <strong>in</strong> thesimulations. The rema<strong>in</strong>der of the thesis addresses whether hydromagnetic <strong>waves</strong> <strong>in</strong> the<strong>core</strong> could be the orig<strong>in</strong> of azimuthal geomagnetic secular variation.Magneto-Rossby <strong>waves</strong> driven by convection (with a dynamical balance between magneticforces, latitude-dependent Coriolis forces, <strong>and</strong> buoyancy forces) are proposed as asuitable c<strong>and</strong>idate for hydromagnetic <strong>waves</strong> <strong>in</strong> the <strong>core</strong>. When driven by thermal convection,such <strong>waves</strong> propagate on the thermal diffusion time scale. Convection-drivenmagneto-Rossby <strong>waves</strong> are found to exhibit dispersive behaviour <strong>and</strong> a dependence ofpropagation speed on latitude. It is shown that such hydromagnetic <strong>waves</strong> <strong>in</strong> the <strong>core</strong>could produce wave-like patterns <strong>in</strong> B r <strong>in</strong> two ways. One mechanism <strong>in</strong>volves the distortionof toroidal magnetic field with<strong>in</strong> the <strong>core</strong> by wave flows produc<strong>in</strong>g new, spatiallyperiodic <strong>and</strong> azimuthally drift<strong>in</strong>g, concentrations of B r . This mechanism is <strong>in</strong>vestigatedus<strong>in</strong>g a 3D, l<strong>in</strong>ear, dynamical model with spherical geometry <strong>and</strong> an imposed toroidalmagnetic field. When this toroidal magnetic field is equatorially symmetric, wave-likepatterns <strong>in</strong> B r centred on the equator are obta<strong>in</strong>ed. Wave flows are found to consist ofalternat<strong>in</strong>g regions of flow convergence <strong>and</strong> divergence close to the outer boundary. Asecond mechanism whereby hydromagnetic <strong>waves</strong> can produce spatially <strong>and</strong> temporallycoherent patterns <strong>in</strong> B r <strong>in</strong>volves advection of exist<strong>in</strong>g B r by the wave flows. This mechanismis studied us<strong>in</strong>g a 1D, diffusionless, analytical model <strong>and</strong> a 2D numerical modelon a spherical surface <strong>in</strong>clud<strong>in</strong>g limited magnetic diffusion. It is found that propagat<strong>in</strong>gconcentrations <strong>in</strong> B r are produced that pulsate <strong>in</strong> amplitude if the wave propagationspeed is faster than the fluid motions with<strong>in</strong> the wave. Both mechanisms could feasiblybe <strong>in</strong>volved <strong>in</strong> produc<strong>in</strong>g the wave-like patterns <strong>in</strong> B r identified at the <strong>core</strong> surface.