The relative importance of the helicity and cross-helicity electromotive dynamo effects for self-sustained magnetic field generation by chaotic thermal convection in rotating spherical shells is investigated as a function of shell thickness. Two distinct branches of dynamo solutions are found to coexist in direct numerical simulations for shell aspect ratios between 0.25 and 0.6 - a mean-field dipolar regime and a fluctuating dipolar regime. The properties characterising the coexisting dynamo attractors are compared and contrasted, including differences in temporal behavior and spatial structures of both the magnetic field and rotating thermal convection. The helicity $α$-effect and the cross-helicity $γ$-effect are found to be comparable in intensity within the fluctuating dipolar dynamo regime, where their ratio does not vary significantly with the shell thickness. In contrast, within the mean-field dipolar dynamo regime the helicity $α$-effect dominates by approximately two orders of magnitude and becomes stronger with decreasing shell thickness.
Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of t…
To understand the generation of the Earth's and planetary magnetic fields, we investigate numerically the combined effect of precession and convection on the dynamo action in a spherical shell. The convection alone, the precession alone and the combined effect of convection and precession are studied at the low Ekman number at which the precessing flow is already unstable. The key result is that although the precession or convection alone is not strong to support the dynamo action the combined effect of precession and convection can support the dynamo action because of the resonance of precess…
Numerical simulations of dynamos in rotating Rayleigh-Bénard convection in plane layers are presented. Two different types of dynamos exist which obey different scaling laws for the amplitude of the magnetic field. The transition between the two occurs within a hydrodynamically uniform regime which can be classified as rapidly rotating convection.
Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, mos…
The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these attractors is established as a function of the rotation parameter \ttau. The width of the basins of attraction is also estimated.
We investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh-Bénard convection using direct numerical simulations. The kinetic and magnetic energies are divided into mean and turbulent components to study the production, transport, and dissipation associated with large and small-scale dynamos. This energy balance-based characterization reveals distinct mechanisms for large- and small-scale magnetic field generation in dynamos, depending on the nature of the velocity field and the conditions imposed at the boundaries.
Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandt…
Simple models of magnetic field generation by convection in rotating spherical shells exhibit properties resembling those observed on the sun. The {assumption of the Boussinesq approximation made in these models} prevents a realistic description of the solar cycle, but through a physically motivated change in the boundary condition for the differential rotation the propagation of dynamo waves towards higher latitudes can be reversed at least at low latitudes.
Natural dynamos such as planets and stars generate global scale magnetic field despite the inferred presence of small scale turbulence. Such systems are known as large scale dynamos and are typically driven by convection and influenced by rotation. Previous numerical studies of rotating dynamos generally find that the large scale magnetic field becomes weaker as the flow becomes more turbulent. The underlying physical processes necessary for sustaining so-called large scale dynamos is therefore still debated. Here we use a suite of numerical simulations to show that strong large scale magnetic…
We present a high-order numerical study of the dependence of the dynamo onset on different electromagnetic boundary conditions, in convecting Boussinesq flows forced by a temperature gradient. Perfectly conducting boundaries, vacuum, and mixed electromagnetic boundary conditions are considered, using a method that treats fields and boundary conditions with close to spectral accuracy. Having one or two conducting boundaries greatly facilitates dynamo action. For the mixed case it is shown that the critical magnetic Reynolds number becomes independent of the Rayleigh number, Ra, for sufficiently…
Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary a…
The value of the Prandtl number $P$ exerts a strong influence on convection-driven dynamos in rotating spherical shells filled with electrically conducting fluids. Low Prandtl numbers promote dynamo action through the shear provided by differential rotation, while the generation of magnetic fields is more difficult to sustain in high-Prandtl-number fluids where higher values of the magnetic Prandtl number $P_m$ are required. The magnetostrophic approximation often used in dynamo theory appears to be valid only for relatively high values of $P$ and $P_m$. Dynamos with a minimum value of $P_m$ s…
Here, an analytical version of numerical results is obtained in case of considering the laminar non-turbulent limit, of a twisted Riemannian thin flux tube. It is shown that the magnetic field is amplified, when electric current helicity and Riemann curvature are both negative. Thus spaces of positive and negative Riemannian curvatures seems to support dynamo action inside the torus, and not only negative Riemannian curvature surfaces as happens in 2D dynamos. New features appear in $α^{2}$-dynamo twisted flow, using the approximation of thin tubes flux tubes. These solutions are obtained in t…
We report the first successful simulation of spontaneous formation of surface magnetic structures from a large-scale dynamo by strongly-stratified thermal convection in Cartesian geometry. The large-scale dynamo observed in our strongly-stratified model has physical properties similar to those in earlier weakly-stratified convective dynamo simulations, indicating that the $α^2$-type mechanism is responsible for it. Additionally to the large-scale dynamo, we find that large-scale structures of the vertical magnetic field are spontaneously formed in the convection zone surface only for the case …
A numerical study of dynamos in rotating convecting plane layers is presented which focuses on magnetic energies and dissipation rates, and the generation of mean fields (where the mean is taken over horizontal planes). The scaling of the magnetic energy with the flux Rayleigh number is different from the scaling proposed in spherical shells, whereas the same dependence of the magnetic dissipation length on the magnetic Reynolds number is found for the two geometries. Dynamos both with and without mean field exist in rapidly rotating convecting plane layers.
A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $α$--$Ω$-type models mainly in two points. First, in addition to the usual $α$ (helicity effect) and $β$ (turbulent magnetic diffusivity), we consider the $γ$ coefficient (c…
Recent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of sign…
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 ins…
Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dy…
Several recent studies have demonstrated how large-scale vortices may arise spontaneously in rotating planar convection. Here we examine the dynamo properties of such flows in rotating Boussinesq convection. For moderate values of the magnetic Reynolds number ($100 \lesssim Rm \lesssim 550$, with $Rm$ based on the box depth and the convective velocity), a large-scale (i.e. system-size) magnetic field is generated. The amplitude of the magnetic energy oscillates in time, nearly out of phase with the oscillating amplitude of the large-scale vortex. The large-scale vortex is disrupted once the ma…
For the understanding of planetary and stellar dynamos an overview of the major parameter dependences of convection driven dynamos in rotating spherical fluid shells is desirable. Although the computationally accessible parameter space is limited, earlier work is extended with emphasis on higher Prandtl numbers and uniform heat flux condition at the outer boundary. The transition from dynamos dominated by non-axisymmetric components of the magnetic field to those dominated by the axisymmetric components depends on the magnetic Prandtl number as well as on the ordinary Prandtl number for higher…
The cross helicity (velocity--magnetic-field correlation) effects in the magnetic-field induction and momentum transport in the magnetohydrodynamic (MHD) turbulence are investigated with the aid of the multiple-scale renormalized perturbation expansion analysis. The outline of the theory is presented with reference to the role of the cross-interaction response functions between the velocity and magnetic field. In this formulation, the expressions of the turbulent fluxes: the turbulent electromotive force (EMF) in the mean induction equation and the Reynolds and turbulent Maxwell stresses in th…
In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal d…
Numerical MHD simulations play increasingly important role for understanding mechanisms of stellar magnetism. We present simulations of convection and dynamos in density-stratified rotating spherical fluid shells. We employ a new 3D simulation code for the solution of a physically consistent anelastic model of the process with a minimum number of parameters. The reported dynamo simulations extend into a "buoyancy-dominated" regime where the buoyancy forcing is dominant while the Coriolis force is no longer balanced by pressure gradients and strong anti-solar differential rotation develops as a…
Rapidly rotating convection-driven dynamos are investigated under different kinematic and magnetic boundary conditions using DNS. At a fixed rotation rate, represented by the Ekman number $E=5\times10^{-7}$, the thermal forcing is varied from 2 to 20 times its value at the onset of convection ($\mathcal{R}=Ra/Ra_c=2-20$), keeping the fluid properties constant ($Pr=Pr_m=1$). The statistical behavior, force balance and heat transport characteristics of the dynamos depend on boundary conditions that dictate both boundary layer and the interior dynamics. At a fixed thermal forcing ($\mathcal{R}=3$…
We study mean-field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and nonzero correlation time ($τ$). We use plane shearing waves in terms of time-dependent exact solutions to the Navier-Stokes equation as derived by Singh \& Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues which yield the growth rate ($γ$) and the cycle period ($P_…
Convective dynamo simulations are performed in local Cartesian geometry. We report the first successful simulation of a large-scale oscillatory dynamo in rigidly rotating convection without stably stratified layers. A key requirement for exciting the large-scale dynamo is a sufficiently long integration time comparable to the ohmic diffusion time. By comparing two models with and without stably stratified layers, their effect on the large-scale dynamo is also studied. The spatiotemporal evolution of the large-scale magnetic field is similar in both models. However, it is intriguing that the ma…
The heat transfer behavior of convection-driven dynamos in a rotating plane layer between two parallel plates, heated from below and cooled from the top, is investigated. At a fixed rotation rate (Ekman Number, $E=10^{-6}$) and fluid properties (thermal and magnetic Prandtl numbers, $Pr=Pr_m=1$), both dynamo convection (DC) and non-magnetic rotating convection (RC) simulations are performed to demarcate the effect of magnetic field on heat transport at different thermal forcings (Rayleigh Number, $Ra=3.83\times10^{9}-3.83\times10^{10}$). In this range, our turbulence resolving simulations demo…
We study dynamo action in a convective layer of electrically-conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly-conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number $R_M$ that is based upon the horizontal integral scale and the horizontally-averaged velocity at the mid-layer of the domain, we find that rota…
Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ($E$), magnetic Prandtl number ($Pm$) and Rayleigh number ($Ra$). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as pert…
Understanding the in situ amplification of large scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity f_h,C has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that f_h,C decreases as the ratio of forcing to large scale wave numbers k_F/k_min increases. From the condition that a large s…
The dynamics of convecting fluids in rotating spherical shells is governed at Prandtl numbers of the order unity by the interaction between differential rotation and roll-like convection eddies. While the differential rotation is driven by the Reynolds stresses of the eddies, its shearing action inhibits convection and causes phenomena such as localized convection and turbulent relaxation oscillations. The response of the system is enriched in the case of dynamo action. Lorentz forces may brake either entirely or partially the geostrophic differential rotation and give rise to two rather diffe…
A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically-modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three timescales that respectively characterize the convective timescale, the large-scale magnetic evolution timescale, and the large-scale thermal evolution timescale. Distinct equations are derived for the cas…
We study dynamo action using numerical simulations of planar Boussinesq convection at rapid rotation (low Ekman numbers, Ek), focusing on subcritical dynamo action in which the dynamo is sustained for Rayleigh numbers, Ra, below the critical Rayleigh number for the onset of nonmagnetic convection, Ra$_c$. These solutions are found by first investigating the supercritical regime, in which the dynamo is able to generate a large-scale magnetic field that significantly influences the convective motions, with an associated Elsasser number of order Ek$^{1/3}$. Subcritical solutions are then found by…
Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significan…
The role of the moments of helicity distribution in rotating turbulence has been studied using the notion of helical distributed chaos. Results of the direct numerical simulations, laboratory experiments and geophysical observations have been used in this investigation. It is shown, in particular, that even for the cases when the global helicity is equal to zero at least even moments are usually non-zero (due to the appearance of the local spatial regions with strong negative and positive helicity) and can play a significant role in the rotating turbulence as adiabatic invariants. Rotating buo…
Using results of laboratory experiments, direct numerical simulations, geomagnetic and solar observations, it is shown that high moments of helicity distribution can dominate power spectra of the magnetic field generated by the magnetohydrodynamic (MHD) dynamo in swirling turbulence even for the cases with zero global helicity. The notion of helical distributed chaos has been used for this purpose.
To study properties of magneto-hydrodynamic (MHD) convection and resultant dynamo activities in proto-neutron stars (PNSs), we construct a "PNS in a box" simulation model with solving compressible MHD equation coupled with a nuclear equation of state (EOS) and a simplified leptonic transport. As a demonstration, we apply it to two types of PNS models with different internal structures: fully-convective model and spherical-shell convection model. By varying the spin rate of models, the rotational dependence of convection and dynamo that operate inside the PNS is investigated. We find that, as a…
Context: Convectively-driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component. Aims: Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability. Methods: The governing equations of three-dimensional nonlinear magnetohydr…
We investigate the dynamo problem in the limit of small magnetic Prandtl number ($\Pm$) using a shell model of magnetohydrodynamic turbulence. The model is designed to satisfy conservation laws of total energy, cross helicity and magnetic helicity in the limit of inviscid fluid and null magnetic diffusivity. The forcing is chosen to have a constant injection rate of energy and no injection of kinetic helicity nor cross helicity. We find that the value of the critical magnetic Reynolds number ($\Rm$) saturates in the limit of small $\Pm$. Above the dynamo threshold we study the saturated regime…
The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities which can be mapped to triad interactions recently identified with facilitating large-scale $α$-type dynamo action and the inverse transfer of magnetic h…
It is shown that helicity dynamics dominates spectral distribution of the velocity fluctuations in turbulent thermal convection at moderate and large values of the Rayleigh number (distributed chaos and scaling respectively). The large-scale circulation (wind) in the turbulent Rayleigh-Bénard convection is especially sensitive to the helicity dynamics and its chaotic reversals can be associated with the reversals of the mean helicity sign (the ergodic restoration of the reflectional symmetry in a long run). Results of the laboratory experiments and measurements in the free atmospheric convecti…
Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in presence of a background linear shear flow. Key techniques involved here are same as in our earlier work \citep[][hereafter paper~I]{JS20}, where we have used the renovating flow based model with shearing waves. Both, the velocity and the helicity fields, are treated as stochastic variables with finite correlation times, $τ$ and $τ_h$, respectively. Growing solutions are obtained when $τ_h > τ$, even when this time-scale separation, characterised by $m=τ_h/τ$, remains below…
It is shown, using results of direct numerical simulations, that the spontaneous breaking of local reflectional symmetry (and corresponding localized kinetic and magnetic helicities) can dominate chaotic dynamics of the small-scale MHD dynamo in the Rayleigh-B{é}nard convection, in kinetically forced flows under strong stratification, in the near-surface solar convection, and in kinetically forced flows at large magnetic Reynolds numbers. The notions of deterministic and helical distributed chaos have been used for this purpose. The coexistence of large- and small-scale dynamo mechanisms and a…
The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations of the 3D magnetohydrodynamic equations. By using the kinetic helicity of the flow as a control parameter, a hysteretic blowout bifurcation is conjectured to be responsible for the transition to dynamo, leading to a sudden increase in the magnetic energy of the attractor. This high-energy hydromagnetic attractor is suddenly destroyed in a boundary crisis when the helicity is decreased. Both the blowout bifurcation and the boundary crisis generate long chaotic transients that are due, respecti…
To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $<{\bf j}\cdot {\bf b}>$) quenche…
We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than…
