Uncovering the dynamical landscape of the geodynamo: a dynamical systems approach

Calum Skene (University of Leeds)

Wednesday 7th May 15:00-16:00
Maths 311B

Abstract

Convection of conducting fluids in planetary interiors is critical for many planetary dynamo processes. Indeed, dynamo action in Earth's conducting liquid outer core is widely believed to be responsible for generating its magnetic field. However, despite extensive research, much is unknown about the origin of this process. One view of this phenomena is that it is a subcritical process, with the Earth’s large scale magnetic field creating a Lorentz force that balances the Coriolis force (magnetostrophic balance). This has the effect of breaking the Taylor-Proudman constraint, allowing the convection needed to sustain a dynamo to set in at a lower Rayleigh number than is required without a magnetic field. This leads to the issue of how to arrive at this strong field solution branch without first increasing the Rayleigh number to values at which a weak magnetic field magnetic is supercritical.

 

In this talk we will discuss dynamical systems approaches for investigating subcriticality of the onset of dynamo action, as well as hydrodynamic convection – providing tools by which the complex dynamical landscape can be decomposed. Through a weakly nonlinear analysis, linear stability results of the onset of convection are extended to provide an amplitude equation valid near criticality. This allows for instabilities to be efficiently characterised as either super- or sub- critical through solving only linear problems. In another approach, nonlinear optimisation will be utilised to find dynamo seeds, small magnetic fields that are able to reach a dynamo solution in a subcritical (although supercritical to convection) regime. Through finding these seeds, pathways through the dynamic landscape by which magnetic fields are amplified can be systematically identified. Emphasis will be placed on developments on the numerical techniques needed for these approaches.

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