Subcritical Behaviour in Rotating Convection and Convectively-Driven Dynamos

Abstract

In planets and stars, convection is thought to be key for generating and maintaining largescale magnetic fields. Many planets possess a hydromagnetic dynamo driven by convective motions, such as the geodynamo. However, a number of smaller planetary bodies, such as Mars, show evidence of once possessing a dynamo that suddenly ceased to exist. One suggested cause for the sudden cessation of the Martian dynamo is that it was operating in a subcritical parameter regime, that is, the dynamo continued to exist when its controlling parameter decreased below the critical value for linear onset, before eventually collapsing towards the non-magnetic trivial state. This thesis aims to explore subcritical behaviour in dynamo action and convection in order to better understand the dynamic processes that affect planetary dynamos. In the first part of this thesis, we focus upon the simpler problem of rotating convection in the absence of a magnetic field. In two-dimensional rotating convection, localised states, known as ‘convectons’, have previously been observed for moderate rotation rates. Convectons are associated with systematic shear flows which locally reduce the inhibiting nature of rotation on convection, potentially promoting subcritical behaviour. We study convectons in 2D Boussinesq convection in a rotating plane layer and perform parametric surveys in both a fully-truncated model with restricted symmetries, and a model where the full horizontal structure is allowed. We successfully obtain rotating convectons for rapid rotation and explore their bifurcation structure, stability and key features. In particular, we show that convectons are typically associated with a full local reduction in the effective rotation. In the second part of this thesis, we study dynamo action using 3D numerical simulations of planar Boussinesq convection at rapid rotation, focussing again on subcritical behaviour. We first generate a large-scale magnetic field in the supercritical regime that significantly influences convective motions. Subcritical solutions are then found by tracking this solution branch into the subcritical regime. Here the dynamo is sustained for convective driving below the critical value for the linear onset of non-magnetic convection. We show that increasing rotation leads to an extension of the subcritical range to an optimal value. At more rapid rotation, subcriticality is then hampered by the emergence of a large-scale convective mode. The inability of the large-scale mode to sustain dynamo action leads to an intermittent behaviour that appears to inhibit subcriticality. Finally, we study the key parameter regimes at which subcritical dynamos exist, such as an optimal magnetic Reynolds number.