I will review some results of dynamos driven by smooth flows and present a study of the growth rate as a function of the magnetic Reynolds number Rm for the whole family of the ABC flows and for 2 different forcing scales. Then I will present results on the non-linear behavior of the dynamo in the infinite Prandtl limit. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field.
The magnetic field of planets or stars is generated by the motion of a conducting fluid through a dynamo instability. The saturation of the magnetic field occurs through the reaction of the Lorentz force on the flow. In relation to this phenomenon, we study the effect of a magnetic field on a turbulent flow of liquid gallium. The measurement of electric potential differences provides a signal related to the local velocity fluctuations. We observe an exponential damping of the turbulent velocity fluctuations as a function of the interaction parameter N. The damping first occurs homogeneously over the whole spectrum of frequencies. For larger values of N, a very strong additional damping occurs at the highest frequencies. However, the injected mechanical power remains independent of the applied magnetic field. The simultaneous measurement of induced magnetic field and electrical potential differences shows a very weak correlation between magnetic field and velocity fluctuations . The observed reduction in the fluctuations is in agreement with a previously proposed mechanism for the saturation of turbulent dynamos and with the order of magnitude of the Von K?rm?n sodium dynamo magnetic field.
In 1999 The Mars Global Surveyor investigated a strong but very heterogeneous crustal magnetization on Mars
mainly localized in the southern hemisphere. These crustal magnetization dichotomy may have either an external or
an internal origin. In the first scenario, the Martian crust was fully magnetized by a dipolar dynamo induced in
the Martian liquid core. After the core dynamo cessation, the crust was demagnetized by volcanoes, impacts or any
other resurfacing event distributed not homogeneously over the surface.
An internal origin due to a magnetizing field, which has already the equivalent equatorial asymmetry is a more
plausible scenario. Here, we link the induction if hemispherical magnetic fields with two key features of the
early Martian interior dynamics into a more realistic model of ancient Martian dynamo. Thermal evolution models
conclude, that there was no chemical contribution to the core convection by freezing outer core's liquid iron.
The dynamo is then driven by pure secular cooling and radioactive decay, what both can be modeled by homogeneous
internal heating.
Due to its small size, the core mantle boundary (CMB) heat flux may be not as homogeneous, as on e.g. Earth.
Mantle convection in smaller planets is thought to develop in larger scales, maybe even single-plume structures.
Also giant impacts might have played a crucial role in the thermal history of Mars, hence they heat up locally
the mantle and the CMB underneath. Therefore, we model the ancient Martian dynamo as rotating, convecting and
conducting fluid heated by an internal heat source and contained in a spherical shell, where the CMB heat flux is
perturbed by a sinusoidal anomaly.
The convection pattern is drastically different from the more classical columnar convection. Because of the
different cooling rates, the northern hemisphere remains hot, while the southern hemisphere is cooled
significantly. Meridional flows from one hemisphere to the other seek to equilibrate the difference in the
temperature. However, the strong Coriolis force diverts these flows in azimuthal direction resulting in force so
called thermal winds. This axisymmetric toroidal flow is retrograde in the northern and prograde in the southern
hemisphere.
In the columnar regime, poloidal and toroidal magnetic fields are produced by helical motions in the individual
columns by a $\alpha$-mechanism. The more the EAA convection dominates, the more vanishes the columnar structure
of the convection. Then both magnetic field contributions decrease simultaneously. But in the EAA mode, the
toroidal field is mainly induced by an $\omega$-effect associated to the shear region between the strong thermal
wind cells. Poloidal field induction is then confined to the southern plumes and much less efficient.
Consequently, the outer boundary field is dominated by small scale patches in the southern hemisphere. The dynamo
character therefore changes from an $\alpha^2$-type in columnar convection to an $\alpha \omega$-type in the EAA
convection.
The Lorentz force tends to supress columnar convection and therefore axisymmetrizes the flow. This increase the
relative importance of the EAA contribution. Since the absolute field strength is lower in the EAA than in the
columnar mode, the Lorentz forces decreases and the columnar mode once more gains in strength.
Averaging in time and extrapolation of the magnetic field to the planetary surface provides constraints on the
magnetization scenarios. Since our results shows a very periodic oscillation of the surface poloidal field in the
pure hemispherical cases of stronger perturbation, the time-averaged field tends to vanish. This might be related
to a dynamo wave similar to Parker waves, where an $\alpha \omega$ mean field dynamo is driven by differential
rotation.
The gas envelopes of Jupiter and Saturn are separated into an outer molecular and an inner metallic
region by a hydrogen phase transition. While the dynamo action takes part in the inner region, the
observed zonal jets are presumably restricted to the outer. Typical numerical models deal with either
the outer region for modeling the observed zonal jets, or the metallic region for modeling the dynamo
effect.
Here we present a holistic approach, simulating both layers together by assuming a radially varying
electrical conductivity. An anelastic approximation allows to incorporate effects of density
stratification.
The results show that the dynamos tend to create dipole-dominated magnetic fields when density
stratification is neglected and the electrical conductivity is homogeneous.
The dipole dominance is lost, however, when the conductivity is decreased in the very outer layer which
confirms the results by Gomez-Perez et. al (2010).
Anelastic simulations with homogeneous electrical conductivities typically yield non-dipolar magnetic
field, even for rather small density scale heights.
The local Rossby number criterion developed by Christensen and Aubert (2006), which successfully
predicts whether a dynamo produces a dipole-dominated field in non-compressible Boussinesq simulations,
does not apply any more in the anelastic case.
The Lorentz forces associated with the magnetic field suppress the strong zonal jets found in
comparable non-magnetic cases. Decreasing the electrical conductivity in the outer layer has now two
effects: the magnetic field becomes once more dipole-dominated and strong zonal jets develop where the
electrical conductivity is low. We therefore conclude that a combination of anelastic effects and
varying electrical conductivity is important for appropriately modeling the interior dynamics of the
gas giants. So far, we have not succeeded in simulating multiple jets as our simulation shows only the
prograde equatorial and the two flanking retrograde jets
We investigate the effect of inhomogeneous layers of magnetic flux on the linear magnetic buoyancy instability. We examine the relationship between the magnetic energy of the layer and the nature of the unstable modes.
We studied numerically the dynamo transition of an incompressible electrically conducting fluid within two concentic spheres, which is driven by the rotation of the inner sphere through no-slip boundary conditions, whereas the outer sphere is stationary. We compared these results with those of an alternative driving mechanism, that drives the fluid in one tenth of the gap width at the inner core in order to investigate the effect of the boundary layer thickness and the equatorial jet on the dynamo threshold in the turbulent regime. The computer code, that is used for these simulations, is a parallelised spectral code by A.Tilgner.
We solve some kinematic fluid dynamo problems in which the magnetic permeability of the solid boundary varies in space. Such a spatial permeability modulation can destabilize some magnetic modes in a flow that would not act as a dynamo otherwise (a 2D flow). An asymptotic expansion for weak permeability modulation confirms the numerical results and sheds some light on the underlying dynamo mechanism. Possible implications for the role of the ferromagnetic impellers of the Von Karman Sodium experiment will be discussed.
The banded structures at the surfaces of Jupiter and Saturn are associated with prograde and retrograde
zonal winds. The depth of these jets remains however poorly known. Theoretical scenarios range from
``shallow models'', that assume that zonal flows are restricted to a very thin layer close to the
surface; to ``deep models'' that suppose that the jets involve the whole
molecular shell (typically $10^4$ kms). The latter idea was supported by fully 3-D numerical
simulations (e.g. Heimpel, 2005) using the Boussinesq approximation, meaning that the background
properties are constant with radius. While this approximation is suitable for liquid iron cores of
planets, it is more questionable in the envelopes of gas giants, where density increases by several
orders of magnitude. The anelastic approximation provides a more realistic framework to simulate the
dynamics of zonal flows as it allows compressibility effects, while filtering out fast acoustic waves
(Lantz & Fan, 1999).
Recent anelastic simulations suggest that including compressibility effects leads to interesting
differences with Boussinesq approaches (Jones, 2009). Here, we therefore adopt an anelastic formulation
to simulate 3-D compressible flows in rapidly rotating shells. We have conducted a systematic
parametric study on the effects of background density stratification and analysed the influences on
both convective flows and zonal jets.
Despite the strong dependence of convection on the density stratification (i.e. the typical lengthscale
of convective flows decreases when compressibility increases), the comparison between Boussinesq and
anelastic simulations reveals striking common features: the latitudinal extent, the amplitude and the
number of zonal jets is found to be nearly independent of
the density stratification, provided convection is strongly driven. Mass-weighted properties of the
flow allows to derive universal scaling laws in the strongly nonlinear regime of convection. Because of
the weak coherence of the convective flow, the additional compressional source of vorticity (Glatzmaier
et al., 2009) hardly affects zonal flow properties.
All theses common features may explain why previous Boussinesq models (e.g. Heimpel et al., 2005) were
already very successful in reproducing the observed morphology of zonal jets in gas giants.
Inspired by the setup of the von-Kármán-Sodium (VKS) dynamo
experiment numerical simulations of the kinematic induction equation have been carried out in a
cylindrical domain. A localized internal distribution of large relative permeability is considered that
represents soft iron material within a conducting fluid flow.
So called paramagnetic pumping at the interface between fluid and soft iron causes a selective
enhancement of the axisymmetric azimuthal field component, ultimately leading to a decoupling between
poloidal and toroidal magnetic field. For moderate magnetic Reynolds numbers, the poloidal component
decays faster than the toroidal part or the simplest non-axisymmetric mode (m1). This effect only
concerns the
necessarily decaying axisymmetric field and does not occur in case of a larger/smaller electrical
conductivity.
The phenomenon requires a particular setup e.g. a thin disk-like
permeability distribution and remains restricted to the axisymmetric field modes. However, these
properties indeed apply to the VKS dynamo.
The separation of poloidal and toroidal modes might be important with regard to mean field dynamo
models of the VKS dynamo since the decoupling effectively disrupts the possibility for a closure of the
dynamo cycle. However, the separation of the axisymmetric field modes can be prevented by an
non-axisymmetric permeability distribution, which might give a hint why dynamo action is absent in
experiments where the fluid flow is driven by an impeller system composed of soft
iron disks and stainless steel blades.
Theoretical studies of the MagnetoRotational Instability (MRI) generally rely on a local description, or
computations between axially infinite (or periodic) cylinders. Since laboratory MRI experiments involve finite
geometries, it is crucial to understand the effect of boundaries on the MRI.
We investigate numerically the flow of an electrically conducting fluid in a cylindrical Taylor-Couette flow when
an axial magnetic field is applied. To minimize Ekman recirculation due to the vertical no-slip boundaries, two
independently rotating rings are used at the top and bottom endcaps. This configuration approximates setup used
in the Princeton MRI experiment, aiming to observe the MagnetoRotational Instability.
Our 3D global simulations show that, in presence of boundaries, the nature of the bifurcation, the non-linear
saturation and the structure of axisymmetric MRI modes are significantly affected by the resultant recirculation.
In addition, large scale non-axisymmetric modes are obtained when the applied field is sufficiently strong. We
show that these modes are related to destabilization of a free shear layer created by the
conjugate action of the applied field and the rotating rings at the endcaps. Similar non-axisymmetric modes are
observed in spherical geometry. Finally, we compare our calculations in cylindrical and spherical geometries to
recent experimental results obtained in the Maryland experiment and the Princeton MRI experiment.
Some geophysic and astrophysic large scale structure, which feature two opposite states, display chaotic reversals between these two states. In order to understand such behaviours,we study experimentally a 2D forced flow which displays a large scale circulation. This circulation exhibits reversals between clockwise and counterclockwise rotation, for high Reynolds number and moderate linear friction. We investigate the mecansims of these reversals and the relation between the mean frequency of the reversals and the linear friction.
In fluctuation flows, fluid particles can have a mean motion in time, even though the Eulerian mean
flow disappears everywhere in space. This phenomenon, known as the Stokes drift plays an essential role
in the problem of magnetic field generation by fluctuation flows at high magnetic Reynolds numbers.
At leading order, we find that the dynamo is generated by the Stokes drift that simply acts as if it
were a mean flow.
We derive this result from a mean-field dynamo theory in
terms of time-averages and this reveals when and how the classical expressions for
alpha and beta tensors recombine into a single Stokes drift
contribution.
In a test-case, we construct fluctuation flows that have a
G.O.Roberts flow as Stokes drift. The fact that we indeed find Roberts' like dynamos and furthermore
good quantitative agreement confirms our statement.
We finally apply the model to prove that a broad class of inertial waves in rapidly rotating flows
cannot drive a dynamo and discuss possible implications for Rossby-waves.
We present a variational data assimilation technique for the Sun using a toy αΩ dynamo model. The purpose of this work is to apply modern data assimilation techniques to solar data using a physically based model. This work represents the first step toward a complete variational model of solar magnetism. We derive the adjoint αΩ dynamo code and use a minimization procedure to invert the spatial dependence of key physical ingredients of the model. We find that the variational technique is very powerful and leads to encouraging results that will be applied to a more realistic model of the solar dynamo.
It is often thought that the fluid dynamics occurring within Earth's liquid metal outer core (and within the magnetic field generating regions of other planets) are governed by two dominant forces: the Coriolis force, resulting from rapid planetary rotation; and the Lorentz force, caused by the resistance of magnetic field lines to bending by flow. These two forces, acting together, are typically thought to reach an equilibrium state known as the magnetostrophic balance. We investigate the role of the Lorentz force in these systems by directly comparing planetary convection models with and without magnetic field generation. Analysis of flow structures in these models reveals, perhaps surprisingly, that the influence of magnetic fields is (in many ways) secondary. We explain this result by reformulating the customary non-dimensional parameter used to define the force balance in a way that is more appropriate to dynamos.
Paleomagnetic measurements of the geomagnetic field reveal a sequence of sudden and occasional global polarity
reversals in the last 160 million years.
Recent self-consistent 3D numerical dynamo simulations replicate many features of the Earth's magnetic field and
several of these models show reversing multipolar regimes of the field.
The study of some statistical properties of geomagnetic reversals is fundamental to understand their origin and
the comparison with numerical dynamo models is helpful to acquire a better knowledge of the geodynamo processes
involved. In this context, we investigate the temporal occurrence of polarity reversals of the dipole field from
Earth's paleomagnetic data and from a numerical dynamo simulation.
Paleomagnetic studies suggest that field intensity drops significantly during a reversal. Numerical simulations
confirm that reversals of the true dipole start when the dynamo switches in a non-dipole-dominated state and end
when it returns to a dipole-dominated configuration. For this reason, in the following analysis, we distinguish
reversals from the normal polarity state in the numerical simulation using the relative contribution of the
dipole to the total field at the core-mantle boundary.
Introducing a statistical quantity that is the suitably normalized local time interval between reversals we test,
for both simulations and geomagnetic data, if the temporal distribution of reversals can be modelled as a
realization of a renewal Poisson process with a time-dependent rate of occurrence, as usually conjectured.
We show that the chaotic dynamics within the numerical dynamo model reproduces the statistical behaviour of
geomagnetic reversals and that the assumed point-like random process is not reliable and must be rejected.
The origin of this failure is due to the presence of clustering in the time sequence of stable polarity epochs,
suggesting a certain amount of memory, due to long-range correlations, in the underlying dynamo process.
A detailed study of the distribution of the intervals of stable polarity epochs will play the key role of
discriminating among all the different processes that can reproduce the observed departure from Poisson
statistics and the degree of long-range memory present.
In this talk, I will discuss the interplay between small- and large-scale dynamo action from the point of view of scale interactions in conducting flows. The implications of multi-scale coupling between the velocity and the magnetic field in magnetohydrodynamic dynamos (in particular, for critical quantities required to sustain magnetic fields, as, e.g., critical Reynolds numbers and critical fractional helicity) will be considered.
I will review recent results on the propagation of Alfvén waves in liquid
metals. After a brief recall of the fundamental properties of Alfvén waves,
I will focus on three main topics:
1) the recent discovery of torsional oscillations (a particular type of
Alfvén waves) in the Earth's core (Gillet et al, Nature, 2010). These
observations provide unique constraints on the magnetic field profile
inside the core.
2) experimental and numerical study of poloïdal Alfvén wave propagation in
a cylinder of liquid metal plunged in an axial magnetic field (Alboussière
et al, 2011).
3) ongoing efforts to unravel the contributions of Coriolis and Lorentz
forces in magnetized Couette flow experiments (Maryland, Princeton,
Grenoble, Dresden).
During the past decades their has been a renewing interest in planetary core dynamics driven by mechanical forcings such as precession, libration and tides. Aside from being possible sources for dynamo action, mechanical forcings may also be responsible for energy dissipation in the liquid layers of the planets as it has been suggested based on astronomical observations. In this presentation, we will give an overview of the recent experimental and numerical progress we made on the flows driven by libration in longitude and latitude in planetary cores and subsurface oceans. In particular, we will show how the viscous and topographic coupling arising from the non-sphericity of the planets can lead to large scale flows as well as space filling turbulence. Finally we will open the discussion on the delicate extrapolation of these results at planetary settings.
We solve the MHD equations for a conducting Boussinesq fluid in a
rotating spherical shell numerically. For one model, the dynamo
coefficients are calculated using the so-called test-field method. These
dynamo coefficients are used in a mean-field calculation in order to
explore the underlying dynamo mechanism.
In particular, the influence of different mechanical boundary conditions is studied. The well known transition
from dipolar to multipolar and eventually oscillatory dynmaos for a local Rossby number of \(Ro_l=0.1\) holds for
any choice of boundary conditions (BCs).
We show that the local Rossby number increases with the aspect ratio, i.e. the ratio of the inner to the outer
sphere radius. Then, considering a particular model with mixed boundary conditions (rigid/stress-free), we show
that this oscillatory dynamo (for Rol>0.1) is of $\alpha^2\Omega$ type. Although the fairly strong differential
rotation of this model influences the magnetic field, the $\Omega$-effect alone is not responsible for its cyclic
time variation. If the $\Omega$-effect is suppressed, the resulting $\alpha^2$-dynamo remains oscillatory.
Surprisingly, the corresponding $\alpha\Omega$-dynamo leads to a non-oscillatory magnetic field. The assumption
of an $\alpha\Omega$-mechanism does not explain the occurrence of magnetic cycles satisfactorily.
Two dynamo branches exist for $Rol<0.1$ and stress-free BCs. The strong-field
branch exhibits similarities with models obtained with rigid BCs whereas the
weak-field branch corresponds to oscillatory dynamos of $\alpha\Omega$-type
having either dipolar or quadrupolar symmetry. These results
could explain observations of stellar magnetic fields, in particular the
fact that stars with the same mass and the same rotation period harbour very
different magnetic fields. But, our models fail to reproduce
coherent cyclic time variations in the high magnetic Reynolds number
regime. This suggests that an additional physical mechanism
plays an important role at least for some stellar dynamos.
I will first review some of the results of the VKS experiment including the recent observation
of localisation of the dynamo magnetic field.
Then, a model will be presented that explains all the behaviors of the magnetic field
observed in the experiment.
The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized effect, which includes both the usual effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized effect scales Rm-1, suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.
I shall review recent work on this topic, including situations with forced turbulence and convective dynamos
We carry out a number of spherical dynamo simulations varying systematically the global rotation rate. Our work examines the dependence of the magnetic field strength on the rotation rate in different dynamo regimes. We also investigate the physical mechanisms leading to changes in the magnetic field scaling for fast and slow rotators. Finally, our results are compared with magnetic field observations of low-mass stars.
The Tayler Instability (TI) is investigated at a liquid metal experiment at Helmholtz-Zentrum Dresden-Rossendorf. The kink-type TI draws its energy from a toroidal magnetic field that becomes unstable against non-axisymmetric perturbations for a sufficiently large field amplitude. TI has been discussed as a possible ingredient of the solar dynamo (Tayler-Spruit dynamo) and as a source of the helical structures in cosmic jets. The experimental setup consists of a cylindrical column of the eutectic alloy GaInSn which can be supplied with an electric current of up to 8 kA. First results of external magnetic field measurements indicate the occurrence of TI at the predicted threshold of the current.
Motions of liquid metal inside the Earth's outer core are responsible for generating the geomagnetic field in a dynamo process. Prominent features in the observed core surface field are intense equatorial flux patches drifting westwards at a rate of 17km/yr. The drift of these features may represent material flow or could perhaps include wave motion. An explanation of these features may provide new information about the hidden part of the magnetic field of the Earth. Our aim is to investigate the formation and dynamics of these flux features in numerical dynamo models. We study a set of numerical dynamo models varying the convection strength by a factor of 150 and ratio of magnetic to viscous diffusivities by a factor of 20 at fixed rapid rotation rate (E=\nu/(2\Omega d^2)=10^{-6}) using a heat flux outer BC. This regime has not been previously thoroughly explored and requires significant computational resources. Our simulations are carried out using a discretisation of degree and order 256 in spherical harmonics, and 516 finite difference points in radius and parallelilized on 516 processors. To investigate to the equatorial dynamics we compute the enstrophy balance which provides insight into how the respective forces contribute to the dynamics of vorticity. We also evaluate the relative contributions of advection, stretching and diffusion in producing secular variation in this region.
The onset of instability of a Boussinesq fluid within a rapidly rotating shell is considered when a
thin unstable layer next to the inner boundary lies beneath a thick stable region which extends to the
outer boundary. As in previous small Ekman number studies, convection takes on the familiar `cartridge
belt' structure which for our model is localised within a thin layer adjacent to (but outside) the
cylinder tangent to the inner sphere at its equator. The azimuthally propagating convective columns,
that the cartridge belt describes, reside entirely within the unstable layer.
We investigate the eigensolutions of the ordinary differential equation governing the axial structure
of the cartridge belt both numerically for moderate (but small) values of the stratification parameter
ε, which measures the width of the unstable layer, and analytically for ε<<1. At the lowest
order of the expansion in powers of ε<<1, the eigenmodes resemble those for classical plane layer
convection, in particular steady (Exchange of stabilities) for large Prandtl number, P>1, and
oscillatory (overstability) with frequency Ω for P<1. At the next order, curvature effects
remove any plane layer degeneracies. Notably, the exchange of stabilities modes oscillate at low
frequency causing the short axial columns to propagate as a wave with a small angular velocity (slow
modes), while the magnitudes of both the Rayleigh number and frequency of the two overstable modes
(fast modes) split. When P<1 the slow modes that exist at large azimuthal
wavenumbers M make a continuous transition to the preferred fast modes at small M.
At all values of P the critical Rayleigh number corresponds to a mode exhibiting prograde propagation,
whether it be a fast or slow mode. This feature is shared by the uniform classical convective shell
models, as well as Busse's celebrated annulus model. None of those models possess any stable
stratification and typically are prone to easily excitable Rossby or inertial modes of convection at
small P. By way of contrast these structures can not exist in our model for small ε due to the
viscous damping in the outer thick stable region.
The DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) will comprise large scale liquid sodium experiments related to geo- and astrophysics as well as experiments for safety and thermohydraulic studies related to sodium fast reactors and liquid metal batteries. The most ambitious parts of DRESDYN are a homogeneous dynamo driven solely by precession, and a large Tayler-Couette type experiment for the combined investigation of the magnetorotational instability and the Tayler instability. After a short summary of our previous achievements we delineate the next steps for the realization of DRESDYN.
In this talk I shall describe some direct statistical simulations (DSS) of astrophysical phenomena such as jets and magnetic instabilities. Solutions of equations based on hierarchies of cumulants will be compared with direct numerical simulations (DNS). Time permitting I shall also describe a technique for the calculation of the turbulent diffusivity of magnetic field.
We present our ongoing work towards the development of a parallel, unstructured finite-volume code for the numerical simulation of incompressible magnetohydrodynamic (MHD) flows. Previously, this code has been used for the study of various MHD flows in the quasi-static regime, i.e. in the limit of vanishing magnetic Reynolds number. Currently, we pursue the further extension of this numerical tool such that it can take into account effects of thermal convection, rotation and magnetic induction. Our eventual aim is to investigate precession-driven dynamos in spheroidal enclosures by means of massively parallel numerical simulations. We first introduce the essential numerical recipes on which our code is based. Then, we illustrate its functionality through two recent case studies. The first one concerns an electrically driven, turbulent quasi-static MHD flow in an annular duct of square cross-section. In the second study, we consider the non-magnetic flow in a precessing sphere.