arXiv subjects

A. Giesecke

Publications and source records attributed to A. Giesecke.

At least 19 recordsLinked to original sources

arXiv2024

Dynamo action driven by precessional turbulence

We reveal and analyze an efficient magnetic dynamo action due to precession-driven hydrodynamic turbulence in the local model of a precessional flow, focusing on the kinematic stage of this dynamo. The growth rate of magnetic field monotonically increases with Poincaré number, $\rm Po$, characterizing precession strength, and magnetic Prandtl number, $\rm Pm$, equal to the ratio of viscosity to resistivity, for the considered ranges of these parameters. The critical ${\rm Po}_c$ for the dynamo onset decreases with increasing $\rm Pm$. To understand the scale-by-scale evolution (growth) of the precession dynamo and its driving processes, we perform spectral analysis by calculating the spectra of magnetic energy and of different terms in the induction equation in Fourier space. To this end, we decompose the velocity field of precession-driven turbulence into 2D vortical and 3D inertial wave modes. It is shown that the dynamo operates across a broad range of scales and exhibits a remarkable transition from a primarily vortex-driven regime at lower $\rm Po$ to a more complex regime at higher $\rm Po$ where it is driven jointly by vortices, inertial waves and the shear of the background precessional flow. The vortices and shear drive the dynamo mostly at large scales, comparable to the flow system size, and at intermediate scales, while at smaller scales it is mainly driven by inertial waves. This study can be important not only for understanding the magnetic dynamo action in precession-driven flows, but also in a general context of flows where vortices emerge and govern the flow dynamics and evolution.

physics.flu-dyn↗

arXiv2023

Numerical and theoretical framework for the DRESDYN precession dynamo experiment

The upcoming DRESDYN (DREsden Sodium facility for DYNnamo and thermohydraulic studies) precession experiment will test the possibility to achieve magnetohydrodynamic dynamo action solely driven by precession. Here, after the description of the experimental facility, we present the results from direct numerical simulations with the aim to understand the flow behavior and its dynamo capability. The main conclusion is that in the nonlinear regime the nutation angle is an essential governing parameter which determines the flow structures and the possibility of dynamo action. We obtain clear indications about the optimum configuration for the future experimental runs.

physics.flu-dyn↗

arXiv2022

Interplay between geostrophic vortices and inertial waves in precession-driven turbulence

The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two dimensional (2D) columnar vortices and three dimensional (3D) inertial waves, whose relative energies depend on the precession parameter $Po$. The vortices resemble the typical condensates of geostrophic turbulence, are aligned along the rotation axis (with zero wavenumber in this direction, $k_z=0$) and are fed by the 3D waves through nonlinear transfer of energy, while the waves (with $k_z\neq0$) in turn are directly fed by the precessional instability of the background flow. The vortices themselves undergo inverse cascade of energy and exhibit anisotropy in Fourier space. For small $Po<0.1$ and sufficiently high Reynolds numbers, the typical regime for most geo- and astrophysical applications, the flow exhibits strongly oscillatory (bursty) evolution due to the alternation of vortices and small-scale waves. On the other hand, at larger $Po>0.1$ turbulence is quasi-steady with only mild fluctuations, the coexisting columnar vortices and waves in this state give rise to a split (simultaneous inverse and forward) cascade. Increasing the precession magnitude causes a reinforcement of waves relative to vortices with the energy spectrum approaching Kolmogorov scaling and, therefore, the precession mechanism counteracts the effects of the rotation.

physics.flu-dyn↗

arXiv2022

Tidally Forced Planetary Waves in the Tachocline of Solar-like Stars

Can atmospheric waves in planet-hosting solar-like stars substantially resonate to tidal forcing? Substantially at a level of impacting the space weather or even of being dynamo-relevant? In particular, low-frequency Rossby waves, which have been detected in the solar near-surface layers, are predestined at responding to sunspot cycle-scale perturbations. In this paper, we seek to address these questions as we formulate a forced wave model for the tachocline layer, which is widely considered as the birthplace of several magnetohydrodynamic planetary waves, i.e., Rossby, inertia-gravity (Poincaré), Kelvin, Alfvén and gravity waves. The tachocline is modeled as a shallow plasma atmosphere with an effective free surface on top that we describe within the Cartesian $β$-plane approximation. As a novelty to former studies, we equip the governing equations with a conservative tidal potential and a linear friction law to account for dissipation. We combine the linearized governing equations to one decoupled wave equation, which facilitates an easily approachable analysis. Analytical results are presented and discussed within several interesting free, damped and forced wave limits for both mid-latitude and equatorially trapped waves. For the idealized case of a single tide generating body following a circular orbit, we derive an explicit analytic solution that we apply to our Sun for estimating leading-order responses to Jupiter. Our analysis reveals that Rossby waves resonating to low-frequency perturbations can potentially reach considerable velocity amplitudes in the order of $10^1 - 10^2\, {\rm cm}\, {\rm s}^{-1}$, which, however, strongly rely on the yet unknown total dissipation.

astro-ph.SR↗

arXiv2022

The effect of nutation angle on the flow inside a precessing cylinder and its dynamo action

The effect of the nutation angle on the flow inside a precessing cylinder is experimentally explored and compared with numerical simulations. The focus is laid on the typical breakdown of the directly forced m=1 Kelvin mode for increasing precession ratio (Poincaré number), and the accompanying transition between a laminar and turbulent flow. Compared to the reference case with a 90° nutation angle, prograde rotation leads to an earlier breakdown, while in the retrograde case the forced mode continues to exist also for higher Poincaré numbers. Depending largely on the occurrence and intensity of an axisymmetric double-roll mode, a kinematic dynamo study reveals a sensitive dependency of the self-excitation condition on the nutation angle and the Poincaré number. Optimal dynamo conditions are found for 90° angle which, however, might shift to slightly retrograde precession for higher Reynolds numbers.

physics.flu-dyn↗

arXiv2020

Schwabe, Gleissberg, Suess-de Vries: Towards a consistent model of planetary synchronization of solar cycles

Aiming at a consistent planetary synchronization model of both short-term and long-term solar cycles, we start with an analysis of Schove's historical data of cycle maxima. Their deviations (residuals) from the average cycle duration of 11.07 years show a high degree of regularity, comprising a dominant 200-year period (Suess-de Vries cycle), and a few periods around 100 years (Gleissberg cycle). Encouraged by their robustness, we support previous forecasts of an upcoming grand minimum in the 21st century. To explain the long-term cycles, we enhance our tidally synchronized solar dynamo model by a modulation of the field storage capacity of the tachocline with the orbital angular momentum of the Sun, which is dominated by the 19.86-year periodicity of the Jupiter-Saturn synodes. This modulation of the 22.14 years Hale cycle leads to a 193-year beat period of dynamo activity which is indeed close to the Suess-de Vries cycle. For stronger dynamo modulation, the model produces additional peaks at typical Gleissberg frequencies, which seem to be explainable by the non-linearities of the basic beat process, leading to a bi-modality of the Schwabe cycle. However, a complementary role of beat periods between the Schwabe cycle and the Jupiter-Uranus/Neptune synodic cycles cannot be completely excluded.

astro-ph.SR↗

arXiv2020

Phase coherence and phase jumps in the Schwabe cycle

Guided by the working hypothesis that the Schwabe cycle of solar activity is synchronized by the 11.07 years alignment cycle of the tidally dominant planets Venus, Earth and Jupiter, we reconsider the phase diagrams of sediment accumulation rates in Lake Holzmaar, and of methanesulfonate (MSA) data in the Greenland ice core GISP2, which are available for the period 10000-9000 cal. BP. Since some half-cycle phase jumps appearing in the output signals are, very likely, artifacts of applying a biologically substantiated transfer function, the underlying solar input signal with a dominant 11.04 years periodicity can be considered as mainly phase-coherent over the 1000 years period in the early Holocene. For more recent times, we show that the re-introduction of a hypothesized "lost cycle" at the beginning of the Dalton minimum would lead to a real phase jump. Similarly, by analyzing various series of $^{14}$C and $^{10}$Be data and comparing them with Schove's historical cycle maxima, we support the existence of another "lost cycle" around 1565, also connected with a real phase jump. Viewed synoptically, our results lend greater plausibility to the starting hypothesis of a tidally synchronized solar cycle, which at times can undergo phase jumps, although the competing explanation in terms of a non-linear solar dynamo with increased coherence cannot be completely ruled out.

astro-ph.SR↗

arXiv2019

Modulated rotating waves in the magnetized spherical Couette system

We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetized spherical Couette system. The set-up consists of a liquid metal confined between two differentially rotating spheres and subjected to an axially applied magnetic field. When the magnetic field strength is varied, several branches of MRW are obtained by means of three dimensional direct numerical simulations (DNS). The MRW originate from parent branches of rotating waves (RW) and are classified according to Rand's (Arch. Ration. Mech. Anal 79:1-37, 182) and Coughling & Marcus (J. Fluid Mech. 234:1-18,1992) theoretical description. We have found relatively large intervals of multistability of MRW at low magnetic field, corresponding to the radial jet instability known from previous studies. However, at larger magnetic field, corresponding to the return flow regime, the stability intervals of MRW are very narrow and thus they are unlikely to be found without detailed knowledge of their bifurcation point. A careful analysis of the spatio-temporal symmetries of the most energetic modes involved in the different classes of MRW will allow in the future a comparison with the HEDGEHOG experiment, a magnetized spherical Couette device hosted at the Helmholtz-Zentrum Dresden-Rossendorf.

physics.flu-dyn↗

arXiv2016

The Tayler instability at low magnetic Prandtl numbers: Chiral symmetry breaking and synchronizable helicity oscillations

The current-driven, kink-type Tayler instability (TI) is a key ingredient of the Tayler-Spruit dynamo model for the generation of stellar magnetic fields, but is also discussed as a mechanism that might hamper the up-scaling of liquid metal batteries. Under some circumstances, the TI involves a helical flow pattern which goes along with some alpha effect. Here we focus on the chiral symmetry breaking and the related impact on the alpha effect that would be needed to close the dynamo loop in the Tayler-Spruit model. For low magnetic Prandtl numbers, we observe intrinsic oscillations of the alpha effect. These oscillations serve then as the basis for a synchronized Tayler-Spruit dynamo model, which could possibly link the periodic tidal forces of planets with the oscillation periods of stellar dynamos.

astro-ph.SR↗

arXiv2016

Synchronized helicity oscillations: a link between planetary tides and the solar cycle?

Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2 perturbation that reflects a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation induced by the Venus--Earth--Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the alpha-effect. Finally, in the framework of a reduced, zero-dimensional alpha--Omega dynamo model we recover a 22.14-year cycle of the solar dynamo.

astro-ph.SR↗

arXiv2015

Triadic resonances in non-linear simulations of a fluid flow in a precessing cylinder

We present results from three-dimensional non-linear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which - in cylindrical geometry - form so-called Kelvin modes. For a precession ratio ${\rm{Po}}=Ω_p/Ω_c=0.014$ the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of ${\rm{Po}}$. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin modes are triggered by non-linear interactions and may constitute a triadic resonance with the fundamental forced mode when the height of the container matches their axial wave lengths. Our simulations reveal triadic resonances at aspect ratios close to those predicted by the linear theory except around the primary resonance of the forced mode. In that regime we still identify various free Kelvin modes, however, all of them exhibit a retrograde drift around the symmetry axis of the cylinder and none of them can be assigned to a triadic resonance. The amplitudes of the free Kelvin modes always remain below the forced mode but may reach up to 6% of the of the container's angular velocity. The properties of the free Kelvin modes will be used in future simulations of the magnetic induction equation to investigate their ability to provide for dynamo action.

physics.flu-dyn↗

arXiv2014

Numerical simulations for the DRESDYN precession dynamo

The next generation dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) will consist of a precessing cylindrical container filled with liquid sodium. We perform numerical simulations of kinematic dynamo action applying a velocity field that is obtained from hydrodynamic models of a precession driven flow. So far, the resulting magnetic field growth-rates remain below the dynamo threshold for magnetic Reynolds numbers up to Rm=2000.

astro-ph.EP↗

arXiv2014

Towards a precession driven dynamo experiment

The most ambitious project within the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) is the set-up of a precession-driven dynamo experiment. After discussing the scientific background and some results of water pre-experiments and numerical predictions, we focus on the numerous structural and design problems of the machine. We also outline the progress of the building's construction, and the status of some other experiments that are planned in the framework of DRESDYN.

physics.flu-dyn↗

arXiv2012

Influence of high permeability disks in an axisymmetric model of the Cadarache dynamo experiment

Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-Kármán-Sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability μ that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rm^c for dynamo action of the first non-axisymmetric mode roughly scales like Rm^c(μ)-Rm^c(μ->infinity) ~ μ^(-1/2) i.e. the threshold decreases as μ increases. This scaling law suggests a skin effect mechanism in the soft iron disks. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high permeability disks which becomes dominant for large μ. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth-rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping at the fluid/disk interface and propose a simplified model that quantitatively reproduces numerical results. The crucial role of the high permeability disks for the mode selection in the Cadarache dynamo experiment cannot be inferred from computations using idealized pseudo-vacuum boundary conditions (H x n = 0).

physics.flu-dyn↗

arXiv2012

Spectral properties of oscillatory and non-oscillatory α^2-dynamos

The eigenvalues and eigenfunctions of a linear α^{2}-dynamo have been computed for different spatial distributions of an isotropic α-effect. Oscillatory solutions are obtained when αexhibits a sign change in the radial direction. The time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue as an oscillatory eigenfunction with conjugate complex eigenvalues. The close proximity of oscillatory and non-oscillatory solutions may serve as the basic ingredient for reversal models that describe abrupt polarity switches of a dipole induced by noise. Whereas the presence of an inner core with different magnetic diffusivity has remarkable little impact on the character of the dominating dynamo eigenmodes, the introduction of equatorial symmetry breaking considerably changes the geometric character of the solutions. Around the dynamo threshold the leading modes correspond to hemispherical dynamos even when the symmetry breaking is small. This behavior can be explained by the approximate dipole-quadrupole degeneration for the unperturbed problem. More complicated scenarios may occur in case of more realistic anisotropies of α- and β-effect or through non-linearities caused by the back-reaction of the magnetic field (magnetic quenching).

astro-ph.EP↗

arXiv2012

DRESDYN - A new facility for MHD experiments with liquid sodium

The DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) is intended as a platform both for large scale experiments related to geo- and astrophysics as well as for experiments related to thermohydraulic and safety aspects of liquid metal batteries and liquid metal fast reactors. The most ambitious projects in the framework of DRESDYN are a homogeneous hydromagnetic dynamo driven solely by precession and a large Taylor-Couette type experiment for the combined investigation of the magnetorotational instability and the Tayler instability. In this paper we give a short summary about the ongoing preparations and delineate the next steps for the realization of DRESDYN.

physics.flu-dyn↗

arXiv2010

Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-Kármán-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence.

physics.flu-dyn↗

arXiv2010

Anisotropic turbulence in weakly stratified rotating magnetoconvection

Numerical simulations of the 3D MHD-equations that describe rotating magnetoconvection in a Cartesian box have been performed using the code NIRVANA. The characteristics of averaged quantities like the turbulence intensity and the turbulent heat flux that are caused by the combined action of the small-scale fluctuations are computed. The correlation length of the turbulence significantly depends on the strength and orientation of the magnetic field and the anisotropic behavior of the turbulence intensity induced by Coriolis and Lorentz force is considerably more pronounced for faster rotation. The development of isotropic behavior on the small scales -- as it is observed in pure rotating convection -- vanishes even for a weak magnetic field which results in a turbulent flow that is dominated by the vertical component. In the presence of a horizontal magnetic field the vertical turbulent heat flux slightly increases with increasing field strength, so that cooling of the rotating system is facilitated. Horizontal transport of heat is always directed westwards and towards the poles. The latter might be a source of a large-scale meridional flow whereas the first would be important in global simulations in case of non-axisymmetric boundary conditions for the heat flux.

astro-ph.EP↗