Christopher A. Jones

A mechanism by which the surface zonal flows of giant planets can be gradually attenuated with depth is explored. The zonal flow is driven by an imposed forcing in a thin layer near the surface. A meridional circulation is set up, analogous to the Ferrel-like cells observed in Jupiter's atmosphere. Acting on a stably stratified thin surface layer, the meridional flow induces a horizontal temperature anomaly which leads to a gradual reduction of the zonal winds with depth, governed by the thermal wind equation. Our model is a Boussinesq plane layer, with gravity acting parallel to the rotation axis. A suite of fully three-dimensional time-dependent numerical simulations has been performed to investigate the model behavior. Below the forced stable layer, convection is occurring, typically in the form of tall thin cells. The fluctuating components of the three-dimensional flow can be driven by either the convection or the Reynolds stresses associated with the jet shear flow. When fluctuations are mainly driven by convection in the form of tall thin columns and the forcing is relatively weak, the horizontal temperature anomaly persists much deeper into the interior than when it is driven by shear flow. The zonal jets can therefore extend deep into the interior, consistent with the Juno gravity data.

Convection driven geodynamo models in rotating spherical geometry have regimes in which reversals occur. However, reversing dynamo models are usually found in regimes where the kinetic and magnetic energy is comparable, so that inertia is playing a significant role in the dynamics. In the Earth's core, the Rossby number is very small, and the magnetic energy is much larger than the kinetic energy. Here we investigate dynamo models in the strong field regime, where magnetic forces have a significant effect on convection. In the core, the strong field is achieved by having the magnetic Prandtl number Pm small, but the Ekman number E extremely small. In simulations, very small E is not possible, but the strong field regime can be reached by increasing Pm. However, if Pm is raised while the fluid Prandtl number is fixed at unity, the most common choice, the Peclet number number becomes small, so that the linear terms in the heat (or composition) equation dominate, which is also far from Earth-like behaviour. Here we increase Pr and Pm together, so that nonlinearity is important in the heat equation and the dynamo is strong field. We find that Earth-like reversals are possible at numerically achievable parameter values, and the simulations have Earth-like magnetic fields away from the times at which it reverses. The magnetic energy is much greater than the kinetic energy except close to reversal times.

Finite-amplitude hydromagnetic Rossby waves in the magnetostrophic regime are studied. We consider the slow mode, which travels in the opposite direction to the hydrodynamic or fast mode, in the presence of a toroidal magnetic field and zonal flow by means of quasi-geostrophic models for thick spherical shells. The weakly nonlinear long waves are derived asymptotically using a reductive perturbation method. The problem at the first order is found to obey a second-order ordinary differential equation, leading to a hypergeometric equation for a Malkus field and a confluent Heun equation for an electrical wire field, and is non-singular when the wave speed approaches the mean flow. Investigating its neutral non-singular eigensolutions for different basic states, we find the evolution is described by the Korteweg–de Vries equation. This implies that the nonlinear slow wave forms solitons and solitary waves. These may take the form of a coherent eddy, such as a single anticyclone. We speculate on the relation of the anticyclone to the asymmetric gyre seen in the Earth's fluid core, and in state-of-the-art dynamo direct numerical simulations.