arXiv subjects

Frank Stefani

Publications and source records attributed to Frank Stefani.

At least 19 recordsLinked to original sources

arXiv2026

Solar and anthropogenic climate drivers: an updated regression model and refined forecast

In a recent paper attempts were made to quantify the respective solar and anthropogenic influences on the terrestrial climate, and to cautiously predict the global mean temperature over the next 130 years. In a double regression analysis, both the binary logarithm of carbon dioxide concentration and the geomagnetic aa-index were used as predictors of the sea surface temperature (SST) since the mid-19th century. The regression results turned out to be sensitive to end effects, leading to a broad range of the climate sensitivity between 0.6 K and 1.6 K per doubling of CO$_2$ when varying the final year. The aim of this paper is to narrow down this range. To this end, the correlations between the two predictors and the dependent variable (SST) are analysed in detail. It is demonstrated that the SST can be predicted until around 2000 almost perfectly using only the aa-index, whereas for later periods the role of CO$_2$ increases significantly. Hence, the weight of the aa-index is fixed to its robust outcome (around 0.04 K/nT) from the regressions up to 1990. The SST data, reduced by the aa-contribution thus specified, are then used in a single regression with CO$_2$ as the only remaining predictor. This results in a significant reduction in the range of CO$_2$ sensitivity, narrowing it to 1.1-1.4 K. Given the exceptionally high temperatures in recent years, these values are considered a kind of upper limit that could still be subject to downward corrections when future data are incorporated. Based on this estimate, the temperature forecast until 2100 is refined by using more precise predictions of the aa-index and the paths of atmospheric CO$_2$ content which are based on constant emission scenarios combined with a linear sink model. With the exception of the most ``pessimistic'' variant, the temperature is predicted to remain below the extraordinarily high value measured in 2024.

physics.ao-ph↗

arXiv2024

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↗

arXiv2022

Synchronizing the helicity of Rayleigh-Bénard convection by a tide-like electromagnetic forcing

We present results on the synchronization of the helicity in a liquid-metal Rayleigh-Bénard (RB) experiment under the influence of a tide-like electromagnetic forcing with azimuthal wavenumber m=2. We show that for a critical forcing strength the typical Large Scale Circulation (LSC) in the cylindrical vessel of aspect ratio unity is entrained by the period of the tide-like forcing, leading to synchronized helicity oscillations with opposite signs in two half-spaces. The obtained experimental results are consistent with and supported by numerical simulations. A similar entrainment mechanism for the helicity in the solar tachocline may be responsible for the astonishing synchronization of the solar dynamo by the 11.07-year triple synodic alignment cycle of the tidally dominant planets Venus, Earth and Jupiter.

physics.flu-dyn↗

arXiv2022

Transient behaviour of electrovortex flow in a cylindrical container

This study is a continuation of the combined experimental and numerical investigation [1] of the flow of the eutectic GaInSn alloy inside a cylindrical vessel exposed to a constant electrical current. The emerging electrovortex flow driven by the interaction of the current, which is applied through a tapered electrode, with its own magnetic field might have both detrimental and advantageous effects in liquid metal batteries. While the former work [1] was mainly concerned with time-averaged results, this paper focuses on the transient behaviour of the electrovortex flow which becomes most relevant under the influence of an external axial field. The additional Lorentz force generated by the interaction of the imposed current with the vertical component of the geomagnetic field bz drives the ordinary electrovortex jet flow into a swirling motion. Velocity distributions and motion characteristics, such as spiral streamlines and shortened and irregularly swinging jet regions, are investigated. The mechanism is analysed in detail for bz = 25.5 μT. The maximum angular velocity of the rotating jet is basically linearly dependent on bz, at least for the values studied here. A good agreement between the transient simulation and the experimental result is shown.

physics.flu-dyn↗

arXiv2021

Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

The focus of this study is to investigate primary and secondary bifurcations to weakly nonlinear flows (weak branch) in convective rotating spheres in a regime where only strongly nonlinear oscillatory sub- and super-critical flows (strong branch) were previously found in [E. J. Kaplan, N. Schaeffer, J. Vidal, and P. Cardin, Phys. Rev. Lett. 119, 094501 (2017)]. The relevant regime corresponds to low Prandtl and Ekman numbers, indicating a predominance of Coriolis forces and thermal diffusion in the system. We provide the bifurcation diagrams for rotating waves (RWs) computed by means of continuation methods and the corresponding stability analysis of these periodic flows to detect secondary bifurcations giving rise to quasiperiodic modulated rotating waves (MRWs). Additional direct numerical simulations (DNS) are performed for the analysis of these quasiperiodic flows for which Poincaré sections and kinetic energy spectra are presented. The diffusion time scales are investigated as well. Our study reveals very large initial transients (more than 30 diffusion time units) for the nonlinear saturation of solutions on the weak branch, either RWs or MRWs, when DNS are employed. In addition, we demonstrate that MRWs have multimodal nature involving resonant triads. The modes can be located in the bulk of the fluid or attached to the outer sphere and exhibit multicellular structures. The different resonant modes forming the nonlinear quasiperiodic flows can be predicted with the stability analysis of RWs, close to the Hopf bifurcation point, by analyzing the leading unstable Floquet eigenmode.

physics.flu-dyn↗

arXiv2021

Conductivity influence on interfacial waves in liquid metal batteries and related two-layer systems

Fluid flows in liquid metal batteries can be generated by a number of effects. We start with a short overview of different driving mechanisms and then address questions specific to the metal pad role instabilities in three-layer systems. We focus on the role of the conductivity distribution in the cell, noting at the same time that interfacial tension should be considered as well for smaller cells. Following this discussion, numerical results on the excitation of interfacial waves in two-layer liquid metal systems with miscibility gaps bearing an interface normal electric current are presented. Confirming recent results from the literature, we find that magnetic damping plays a decisive role for strong vertical magnetic fields. In addition, boundary conditions for the electric field strongly influence critical currents and growth rates.

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↗

arXiv2021

Multiple regression analysis of anthropogenic and heliogenic climate drivers, and some cautious forecasts

The two main drivers of climate change on sub-Milankovic time scales are re-assessed by means of a multiple regression analysis. Evaluating linear combinations of the logarithm of carbon dioxide concentration and the geomagnetic aa-index as a proxy for solar activity, we reproduce the sea surface temperature (HadSST) since the middle of the 19th century with an adjusted $R^2$ value of around 87 per cent for a climate sensitivity (of TCR type) in the range of 0.6 K until 1.6 K per doubling of CO$_2$. The solution of the regression is quite sensitive: when including data from the last decade, the simultaneous occurrence of a strong El Niño on one side and low aa-values on the other side lead to a preponderance of solutions with relatively high climate sensitivities around 1.6 K. If those later data are excluded, the regression leads to a significantly higher weight of the aa-index and a correspondingly lower climate sensitivity going down to 0.6 K. The plausibility of such low values is discussed in view of recent experimental and satellite-borne measurements. We argue that a further decade of data collection will be needed to allow for a reliable distinction between low and high sensitivity values. Based on recent ideas about a quasi-deterministic planetary synchronization of the solar dynamo, we make a first attempt to predict the aa-index and the resulting temperature anomaly for various typical CO$_2$ scenarios. Even for the highest climate sensitivities, and an unabated linear CO$_2$ increase, we predict only a mild additional temperature rise of around 1 K until the end of the century, while for the lower values an imminent temperature drop in the near future, followed by a rather flat temperature curve, is prognosticated.

physics.ao-ph↗

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

Zero net flux MRI-turbulence in disks $-$ sustenance scheme and magnetic Prandtl number dependence

We investigate sustenance and dependence on magnetic Prandtl number (${\rm Pm}$) for magnetorotational instability (MRI)-driven turbulence in astrophysical Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space -- the nonlinear transverse cascade -- which is generic to shear flows and fundamentally different from usual direct/inverse cascade. The zero flux MRI has no exponentially growing modes, so its growth is transient, or nonmodal. Turbulence self-sustenance is governed by constructive cooperation of the transient growth of MRI and the nonlinear transverse cascade. This cooperation takes place at small wavenumbers (on the flow size scales) referred to as the vital area in Fourier space. The direct cascade transfers mode energy from the vital area to larger wavenumbers. At large ${\rm Pm}$, the transverse cascade prevails over the direct one, keeping most of modes' energy contained in small wavenumbers. With decreasing ${\rm Pm}$, however, the action of the transverse cascade weakens and can no longer oppose the action of direct cascade which more efficiently transfers energy to higher wavenumbers, leading to increased resistive dissipation. This undermines the sustenance scheme, resulting in the turbulence decay. Thus, the decay of zero net flux MRI-turbulence with decreasing ${\rm Pm}$ is attributed to topological rearrangement of the nonlinear processes when the direct cascade begins to prevail over the transverse cascade.

astro-ph.HE↗

arXiv2020

Experimental investigation of the return flow instability in magnetic spherical Couette flow

We conduct magnetic spherical Couette (MSC) flow experiments in the return flow instability regime with GaInSn as the working fluid, and the ratio of the inner to the outer sphere radii $r_{\rm i}/r_{\rm o} = 0.5$, the Reynolds number ${\rm Re} = 1000$, and the Hartmann number ${\rm Ha} \in [27.5,40]$. Rotating waves with different azimuthal wavenumbers $m \in \{2, 3, 4\}$ manifest in certain ranges of ${\rm Ha}$ in the experiments, depending on whether the values of ${\rm Ha}$ were fixed or varied from different initial values. These observations demonstrate the multistability of rotating waves, which we attribute to the dynamical system representing the state of the MSC flow tending to move along the same solution branch of the bifurcation diagram when ${\rm Ha}$ is varied. In experiments with both fixed and varying ${\rm Ha}$, the rotation frequencies of the rotating waves are consistent with the results of nonlinear stability analysis. A brief numerical investigation shows that differences in the azimuthal wavenumbers of the rotating waves that develop in the flow also depend on the azimuthal modes that are initially excited.

physics.flu-dyn↗

arXiv2020

Shaken and stirred: When Bond meets Suess-de Vries and Gnevyshev-Ohl

We argue that the most prominent temporal features of the solar dynamo, in particular the Hale cycle, the Suess-de Vries cycle (associated with variations of the Gnevyshev-Ohl rule), Gleissberg-type cycles, and grand minima can be self-consistently explained by double synchronization with the 11.07-years periodic tidal forcing of the Venus-Earth-Jupiter system and the (mainly) 19.86-years periodic motion of the Sun around the barycenter of the solar system. In our numerical simulation, grand minima, and clusters thereof, emerge as intermittent and non-periodic events on millennial time scales, very similar to the series of Bond events which were observed throughout the Holocene and the last glacial period. If confirmed, such an intermittent transition to chaos would prevent any long-term prediction of solar activity, notwithstanding the fact that the shorter-term Hale and Suess-de Vries cycles are clocked by planetary motion.

astro-ph.SR↗

arXiv2020

Generating a tide-like flow in a cylindrical vessel by electromagnetic forcing

We show and compare numerical and experimental results on the electromagnetic generation of a tide-like flow structure in a cylindrical vessel which is filled with the eutectic liquid metal alloy GaInSn. Fields of various strengths and frequencies are applied to drive liquid metal flows. The impact of the field variations on amplitude and structure of the flows is investigated. The results represent the basis for a future Rayleigh-Bénard experiment, in which a modulated tide-like flow perturbation is expected to synchronize the typical sloshing mode of the large-scale circulation. A similar entrainment mechanism for the helicity in the Sun may be responsible for the synchronization of the solar dynamo with the alignment cycle of the tidally dominant planets Venus, Earth and Jupiter.

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

Convection-Caused Symmetry Breaking of Azimuthal Magnetorotational Instability in a Liquid Metal Taylor-Couette Flow

We report the results of a liquid metal Taylor-Couette experiment in the Rayleigh-stable regime under the influence of an azimuthal magnetic field. We observe that the resulting azimuthal magnetorotational instability (AMRI) from our experimental setup is significantly influenced by the thermal boundary conditions. Even a minimal radial heat flux leads to a symmetry breaking, which results in the AMRI waves traveling either upwards or downwards. We identify the thermal radiation by the central axial current as the heat source responsible for vertical convection in the liquid. Preliminary numerical investigations point towards an interaction between AMRI and thermal convection, which supports our experimental findings.

physics.app-ph↗