Semi-convection in rotating spherical shells: flows, layers and dynamos

Large regions of giant planets are thought to possess unstable thermal gradients stabilised by gradients in heavy-element composition. The fluid can then develop semi-convection, a double-diffusive instability driven by the unequal molecular diffusivities of heat and composition. While previous studies have focus mainly on local Cartesian models, we investigate semi-convection in rotating spherical shells, the geometry relevant to planetary interiors, using direct numerical simulations In a first nonlinear phase, the flow spontaneously forms concentric density staircases composed of well-mixed layers separated by thin, strongly stratified interfaces. We propose scalings for both the thickness of these layers and their survival time in terms of the rotation rate and stratification. Over longer timescales, layers merge to produce statistically steady states consisting either of a fully convective shell or of a convective layer ovelain by a persistent stably stratified layer (SSL), depending on the balance between stratification and rotational constraint. This shows that a layer subject to a semi-convection instability can self-organise into a convective layer and a SSL. These layers can generate a self-sustained magnetic field. Our dynamo simulations show that magnetic fields generated within the turbulent convective region are filtered by zonal flows in the overlying SSL, resulting in strongly a dipolar and axisymmetric external field, in encouraging agreement with Saturn's magnetic field. Across the explored parameter range, both the Rossby number and the thickness of the stably stratified layer are governed by a single combination of control parameters. This enable identification of a regime favourable to planetary-like dynamos.