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Register a new userGrowth rate degeneracies in kinematic dynamos
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We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudo-vacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into -u. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by Dudley and James (1989). Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different.
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Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva et al., 2019, Geophys. Astrophys. Fluid Dyn., doi:10.1080/03091929.2019.1640875) are found to persist significantly beyond the onset of instability while their regime transitions remain abrupt. In the semi-convecting and the fingering regimes characteristic flow velocities are small compared to those in the thermally- and compositionally-dominated overturning regimes, while zonal flows remain weak in all regimes apart from the thermally-dominated one. Compositionally-dominated overturning convection exhibits significantly narrower azimuthal structures compared to all other regimes while differential rotation becomes the dominant flow component in the thermally-dominated case as driving is increased. Dynamo action occurs in all regimes apart from the regime of fingering convection. While dynamos persist in the semi-convective regime they are very much impaired by small flow intensities and very weak differential rotation in this regime which makes poloidal to toroidal field conversion problematic. The dynamos in the thermally-dominated regime include oscillating dipolar, quadrupolar and multipolar cases similar to the ones known from earlier parameter studies. Dynamos in the compositionally-dominated regime exhibit subdued temporal variation and remain predominantly dipolar due to weak zonal flow in this regime. These results significantly enhance our understanding of the primary drivers of planetary core flows and magnetic fields.
Convective flows coupled with solidification or melting in water bodies play a major role in shaping geophysical landscapes. Particularly in relation to the global climate warming scenario, it is essential to be able to accurately quantify how water-body environments dynamically interplay with ice formation or melting process. Previous studies have revealed the complex nature of the icing process, but have often ignored one of the most remarkable particularity of water, its density anomaly, and the induced stratification layers interacting and coupling in a complex way in presence of turbulence and phase change. By combining experiments, numerical simulations, and theoretical modeling, we investigate solidification of freshwater, properly considering phase transition, water density anomaly, and real physical properties of ice and water phases, which we show to be essential for correctly predicting the different qualitative and quantitative behaviors. We identify, with increasing thermal driving, four distinct flow-dynamics regimes, where different levels of coupling among ice front, stably and unstably stratified water layers occur. Despite the complex interaction between the ice front and fluid motions, remarkably, the average ice thickness and growth rate can be well captured with the theoretical model. It is revealed that the thermal driving has major effects on the temporal evolution of the global icing process, which can vary from a few days to a few hours in the current parameter regime. Our model can be applied to general situations where the icing dynamics occurs under different thermal and geometrical conditions (e.g. cooling conditions or water layer depth).
Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.
Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independent flow to flows with a strong poloidal component and lesser symmetry are found. It is shown that all flow regimes characterised with significant non-axisymmetric components are capable of generating self-sustained magnetic field. As the value of the Prandtl number is decreased and the value of the Ekman number is decreased flows become strongly time-dependent with progressively complex spatial structure and dynamos can be generated at lower values of the magnetic Prandtl number.
We study generation of magnetic fields, involving large spatial scales, by convective plan-forms in a horizontal layer. Magnetic modes and their growth rates are expanded in power series in the scale ratio, and the magnetic eddy diffusivity (MED) tensor is derived for flows, symmetric about the vertical axis in a layer. For convective rolls magnetic eddy correction is demonstrated to be always positive. For rectangular cell patterns, the region in the parameter space of negative MED coincides with that of small-scale magnetic field generation. No instances of negative MED in hexagonal cells are found. A family of plan-forms with a smaller symmetry group than that of rectangular cell patterns has been found numerically, where MED is negative for molecular magnetic diffusivity over the threshold for the onset of small-scale magnetic field generation.
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