arXiv subjects

André Giesecke

Publications and source records attributed to André Giesecke.

11 recordsLinked to original sources

arXiv2025

The role of magnetic boundaries in kinematic and self-consistent magnetohydrodynamic simulations of precession-driven dynamo action in a closed cylinder

We numerically examine dynamo action generated by a flow of an electrically conducting fluid in a precessing cylindrical cavity. We compare a simplified kinematic approach based on the solution of the magnetic induction equation with a prescribed velocity field with the results from a self-consistent three-dimensional simulation of the complete set of magnetohydrodynamic equations. In all cases, we observe a minimum for the onset of dynamo action in a transitional regime, within which the hydrodynamic flow undergoes a change from a large-scale to a more small-scale, turbulent behaviour. However, significant differences in the absolute values for the critical magnetic Reynolds number occur depending on the physical properties of the external layers surrounding the flow active domain. The strong influence of the electromagnetic properties of outer layers with the large variation of the critical magnetic Reynolds number can be related to the existence of two different branches with dynamo action. In contrast to the kinematic models, the nonlinear MHD simulations reveal a small scale dynamo solution with the magnetic energy remaining significantly smaller than the kinetic energy of the flow. In irregular intervals, we observe dynamo bursts with a local concentration of the magnetic field, resulting in a global increase of the magnetic energy by a factor of 3 to 5. However, diffusion of the local patches caused by strong local shear is too rapid, causing these features to exist for only a short period so that their dynamical impact on the dynamo remains small.

physics.flu-dyn↗

arXiv2024

The global flow state in a precessing cylinder

We examine the fluid flow forced by precession of a rotating cylindrical container using numerical simulations and experimental flow measurements with ultrasonic Doppler velocimetry (UDV). The analysis is based on the decomposition of the flow field into contributions with distinct azimuthal symmetry or analytically known inertial modes and the corresponding calculation of their amplitudes. We show that the predominant fraction of the kinetic energy of the precession-driven fluid flow is contained only within a few large-scale modes. The most striking observation shown by simulations and experiments is the transition from a flow dominated by large-scale structures to a more turbulent behaviour with the small-scale fluctuations becoming increasingly important. At a fixed rotation frequency (parametrized by the Reynolds number, ${\rm{Re}}$) this transition occurs when a critical precession ratio is exceeded and consists of a two-stage collapse of the directly driven flow going along with a massive modification of the azimuthal circulation (the zonal flow) and the appearance of an axisymmetric double-roll mode limited to a narrow range of precession ratios. A similar behaviour is found in experiments which make it possible to follow the transition up to Reynolds numbers of ${\rm{Re}}\approx 2\times 10^6$. We find that the critical precession ratio decreases with rotation, initially showing a particular scaling $\propto {\rm{Re}}^{-\frac{1}{5}}$ but developing an asymptotic behaviour for ${\rm{Re}}\gtrsim 10^5$ which might be explained by the onset of turbulence in boundary layers.

physics.flu-dyn↗

arXiv2023

High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows

The magnetised spherical Couette (MSC) problem, a three dimensional magnetohydrodynamic paradigmatic model in geo- and astrophysics, is considered to investigate bifurcations to high-dimensional invariant tori and chaotic flows in large scale dissipative dynamical systems with symmetry. The main goal of the present study is to elucidate the origin of chaotic transients and intermittent behaviour from two different sequences of Hopf bifurcations involving invariant tori with four fundamental frequencies, which may be resonant. Numerical evidence of the existence of a crisis event destroying chaotic attractors and giving rise to the chaotic transients is provided. It is also shown that unstable invariant tori take part in the time evolution of these chaotic transients. For one sequence of bifurcations, the study demonstrates that chaotic transients display on-off intermittent behaviour. A possible explanatory mechanism is discussed.

physics.flu-dyn↗

arXiv2021

Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow

The existence of triadic resonances in the magnetized spherical Couette system (MSC) is related to the development of modulated rotating waves, which are quasiperiodic flows understood in terms of bifurcation theory in systems with symmetry. In contrast to previous studies in spherical geometry the resonant modes are not inertial waves but related with the radial jet instability which is strongly equatorially antisymmetric. We propose a general framework in which triadic resonances are generated through successive Hopf bifurcations from the base state. The study relies on an accurate frequency analysis of different modes of the flow, for solutions belonging to two different bifurcation scenarios. The azimuthal and latitudinal nonlinear coupling among the resonant modes is analysed and interpreted using spherical harmonics and the results are compared with previous studies in spherical geometry.

physics.flu-dyn↗

arXiv2020

Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system

The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical setup is exposed to an axial magnetic field. The classical Fourier Transform method provides a first estimation of the time dependence of the frequencies associated to the flow, as well as its volume-averaged properties. It is however unable to detect strange attractors close to regular solutions in the Feigenbaum as well as Newhouse-Ruelle-Takens bifurcation scenarios. It is shown that Laskar's frequency algorithm is sufficiently accurate to identify these strange attractors and thus is an efficient tool for classification of chaotic flows in high dimensional dynamical systems. Our analysis of several chaotic solutions, obtained at different magnetic field strengths, reveals a strong robustness of the main frequency of the flow. This frequency is associated to an azimuthal drift and it is very close to the frequency of the underlying unstable rotating wave. In contrast, the main frequency of volume-averaged properties can vary almost one order of magnitude as the magnetic forcing is decreased. We conclude that, at the moderate differential rotation considered, unstable rotating waves provide a good description of the variation of the main time scale of any flow with respective variations in the magnetic field.

physics.flu-dyn↗

arXiv2020

Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking

The occurrence of magnetohydrodynamic (MHD) quasiperiodic flows with four fundamental frequencies in differentially rotating spherical geometry is understood in terms of a sequence of bifurcations breaking the azimuthal symmetry of the flow as the applied magnetic field strength is varied. These flows originate from unstable periodic and quasiperiodic states with broken equatorial symmetry but having four-fold azimuthal symmetry. A posterior bifurcation gives rise to two-fold symmetric quasiperiodic states, with three fundamental frequencies, and a further bifurcation to a four-frequency quasiperiodic state which has lost all the spatial symmetries. This bifurcation scenario may be favoured when differential rotation is increased and periodic flows with $m$-fold azimuthal symmetry, $m$ being product of several prime numbers, emerge at sufficiently large magnetic field.

physics.flu-dyn↗

arXiv2020

Chaotic wave dynamics in weakly magnetised spherical Couette flows

Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak externally applied axial magnetic field (measured by the Hartmann number Ha). By varying the latter a rich variety of flow features, both in terms of spatial symmetry and temporal dependence, is obtained. Flows with two or three independent frequencies describing their time evolution are found as a result of Hopf bifurcations. They are stable on a sufficiently large interval of Hartmann numbers where regions of multistability of two, three and even four types of these different flows are detected. The temporal character of the solutions is analysed by means of an accurate frequency analysis and Poincaré sections. An unstable branch of flows undergoing a period doubling cascade and frequency locking of three-frequency solutions is described as well.

physics.flu-dyn↗

arXiv2019

A model of a tidally synchronized solar dynamo

We discuss a solar dynamo model of Tayler-Spruit type whose Omega-effect is conventionally produced by a solar-like differential rotation but whose alpha-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07 years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14 years period or pulsating with a 11.07 years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of alpha, we prove the subcritical nature of this Tayler-Spruit type dynamo. The resulting amplitude of the alpha oscillation that is required for dynamo action turns out to lie in the order of 1 m/s, which seems not implausible for the sun. When starting with a more classical, non-periodic part of alpha, even less of the oscillatory alpha part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behaviour during the Maunder minimum, can be easily triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres.

astro-ph.SR↗

arXiv2017

On the synchronizability of Tayler-Spruit and Babcock-Leighton type dynamos

The solar cycle appears to be remarkably synchronized with the gravitational torques exerted by the tidally dominant planets Venus, Earth and Jupiter. Recently, a possible synchronization mechanism was proposed that relies on the intrinsic helicity oscillation of the current-driven Tayler instability which can be stoked by tidal-like perturbations with a period of 11.07 years. Inserted into a simple alpha-Omega dynamo model these resonantly excited helicity oscillations led to a 22.14 years dynamo cycle. Here, we assess various alternative mechanisms of synchronization. Specifically we study a simple time-delay model of Babcock-Leighton type dynamos and ask whether periodic changes of either the minimal amplitude for rising toroidal flux tubes or the Omega effect could eventually lead to synchronization. In contrast to the easy and robust synchronizability of Tayler-Spruit dynamo models, our answer for those Babcock-Leighton type models is less propitious.

astro-ph.SR↗

arXiv2017

Magnetic field dynamos and magnetically triggered flow instabilities

The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear. In this paper, the main results of these two projects are summarized.

physics.flu-dyn↗

arXiv2017

The DRESDYN project: planned experiments and present status

The Dresden sodium facility for dynamo and thermohydraulic studies (DRESDYN) is a platform for large-scale liquid sodium experiments devoted to fundamental geo- and astrophysical questions as well as to various applied problems related to the conversion and storage of energy. Its most ambitious part is a precession driven dynamo experiment comprising 8 tons of liquid sodium supposed to rotate with up to 10 Hz and to precess with up to 1 Hz. Another large-scale set-up is a Tayler-Couette experiment with a gap width of 0.2 m and a height of 2 m, whose inner cylinder rotates with up to 20 Hz. Equipped with a coil system for the generation of an axial field of up to 120 mT and two different axial currents through the center and the liquid sodium, this experiment aims at studying various versions of the magnetorotational instability and their combinations with the Tayler instability. We discuss the physical background of these two experiments and delineate the present status of their technical realization. Other installations, such as a sodium loop and a test stand for In-Service-Inspection experiments will also be sketched.

physics.flu-dyn↗