UK MHD 2013 will feature two Invited Lectures on major directions of current research in magnetohydrodynamics. We are proud to present our distinguished Invited Speakers:
- WITHDRAWN: Prof. M.R.E. Proctor, FRS - DAMTP, University of Cambridge, UK
Title of Lecture: "Mean field electrodynamics: its glorious past and uncertain future"
Abstract: Mean-field electrodynamics was conceived as a model of dynamo action on large scales due to small scale velocity fields. The model equations for the mean field, which can give growing solutions in axisymmetric geometries (thus circumventing Cowling's Theorem), have led to a very large number of analytical and numerical studies, and have produced plausible descriptions of the solar magnetic cycle. The underlying theory is undoubtedly correct in some parameter ranges but problems arise when there is the possibility of dynamo action on the smallest scales. In addition there are difficulties in extending the models into the nonlinear regime, where Lorentz forces affect the flow. I will review the history of the model, investigate its theoretical underpinning and will discuss the implications of recent work.
- Prof. Chris A. Jones - School of Mathematics, University of Leeds, UK
Title of Lecture: "Dynamo models of Jupiter's magnetic field"
Abstract: Numerical dynamo models have had some success in reproducing important features of the Earth's magnetic field. Here we report on simulations of Jupiter's magnetic field using the anelastic approximation, which takes into account the large density variation across the dynamo region. The reference state used in these models is a Jupiter model taken from ab initio calculations of the physical properties of Jupiter's magnetic field (French et al. 2012), which makes the reasonable assumption that the interior is close to adiabatic. The French et al. work also gives an electrical conductivity profile which is adopted here. Dynamo simulations depend on the dimensionless input parameters, partibularly the Ekman number, Rayleigh number, the Prandtl number and magnetic Prandtl number. Many different types of field have been found, some of which will be described. The most relevant models are those which produce a Jupiter-like strong dipole dominated field. These are found at low Ekman number, Rayleigh numbers large enough for the convective heat flux to dominate the radiative flux, flow Prandtl number and moderate magnetic Prandtl number. Another important issue is the driving heat flux source. Here we assume that Jupiter evolves through a sequence of adiabats, leading to a distributed entropy source throughout the planet, rather than basal heating from the small rocky core. The interaction between the magnetic field, the zonal flow and the convection appears to be crucial in determining the type of magnetic field found.
Title of Lecture: "Asymptotic solution of a kinematic αΩ-dynamo with meridional circulation"
Co-authors: Andrew P. Bassom, K. Kuzanyan and D. Sokoloff
Abstract: Many stars exhibit magnetic cycles typified by the butterfly diagram characterising our sun's 11 year solar activity cycle. Parker explained the phenomenon by an αΩ-dynamo acting in the star's convection zone causing the equatorial propagation of dynamo waves. In contrast, to the many continuing numerical investigations, we adopt a minimalist approach and expand on Parker's original one-dimensional uniform plane layer model. To apply asymptotic methods, we suppose that the dynamo is confined to a thin shell with latitudinal variations of the αΩ-sources, whose product the Dynamo number vanishes at the pole and equator. The ensuing linear stability problem is resolved by global stability criteria. Our new results concern the role of meridional circulation. They show that sufficiently large circulation halts the Parker travelling waves leading to non-oscillatory behaviour, a result only predicted previously from numerical integration of the full pde's governing axisymmetric αΩ-dynamos.