The effect of inertia on the equilibration of non-linear αω and α[superscript 2]ω dynamo models

The objective of this thesis is to understand more about the role of inertia in the Earth’s dynamo. Studies of 2.5D and 3D dynamo models have reported finding dynamo action increasingly difficult to maintain as the strength of inertia measured by the Rossby number, Ro, is increased, (see for example, Fearn and Morrison (2001) or Christensen et al (1999)). Fearn and Rahman (2004b) considered a non-linear mean-field a2-type dynamo model and investigated the effect inertia has on solutions. In their axisymmetric model, the effects of a non-axisymmetric flow are introduced to the problem via the so-called a-effect, which generates poloidal magnetic field through twisting the toroidal field lines. In the a2-type model, this effect also generates toroidal field from poloidal field. Fearn and Rahman (2004b) found that, as the strength of the inertia, Ro was increased, dynamo action was enabled to occur more easily. The non-axisymmetric generation process (i.e. the a-effect) is unaffected by Ro. In the 2.5D/3D models the dynamo process is driven through internal convection. Increasing the strength of inertia, as considered by Fearn and Morrison (2001) and Christensen et al (1999), reveals that dynamo action shuts off if Ro becomes too large. In the 2.5D/3D models, inertia affects convection as well as the dynamo equilibration process. Due to the complexity of the 2.5D/3D models, varying a single parameter e.g. Rossby number, influences the overall dynamo process in a number of different ways making it difficult to understand the different physical mechanisms acting to equilibrate the dynamo. This led to our present studies of non-linear aw and a2w-type dynamo models. These models are intermediate to the a2-type model and the 2.5D/3D models as we include a buoyancy driving, but instead of it being dynamically determined as in the hydrodynamic model, we choose to prescribe it, in an effort to further disentangle the complex processes in the dynamo mechanism and the role inertia plays