arXiv subjects

F. Stefani

Publications and source records attributed to F. Stefani.

At least 37 records · Page 2Linked to original sources

arXiv2022

Numerical simulation of tidal synchronization of the large-scale circulation in Rayleigh-Bénard convection with aspect ratio 1

A possible explanation for the apparent phase stability of the 11.07-year Schwabe cycle of the solar dynamo was the subject of a series of recent papers. The synchronization of the helicity of an instability with azimuthal wavenumber m=1 by a tidal m=2 perturbation played a key role here. To analyze this type of interaction in a paradigmatic set-up, we study a thermally driven Rayleigh-Bénard Convection (RBC) of a liquid metal under the influence of a tide-like electromagnetic forcing. As shown previously, the time-modulation of this forcing emerges as a peak frequency in the m=2 mode of the radial flow velocity component. In this paper we present new numerical results on the interplay between the Large Scale Circulation (LSC) of a RBC flow and the time modulated electromagnetic forcing.

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↗

arXiv2022

From helical to standard magnetorotational instability: predictions for upcoming liquid sodium experiments

We conduct a linear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard version (SMRI) with a purely axial background magnetic field and two further types -- helically modified SMRI (H-SMRI) and helical MRI (HMRI) -- in the presence of combined axial and azimuthal magnetic fields. This study is intended as preparatory for upcoming large-scale liquid sodium MRI experiments planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so we explore these instability types for typical values of the main parameters: the magnetic Reynolds number, the Lundquist number and the ratio of the angular velocities of the cylinders, which are attainable in these experiments. In contrast to previous attempts at detecting MRI in the lab, our results demonstrate that SMRI and its helically modified version can in principle be detected in the DRESDYN-TC device for the range of the above parameters, including the astrophysically most important Keplerian rotation, despite the extremely small magnetic Prandtl number of liquid sodium. Since in the experiments we plan to approach (H-)SMRI from the previously studied HMRI regime, we characterise the continuous and monotonous transition between the both regimes. We show that H-SMRI, like HMRI, represents an overstability (travelling wave) with non-zero frequency linearly increasing with azimuthal field. Because of its relevance to finite size flow systems in experiments, we also analyse the absolute form of H-SMRI and compare its growth rate and onset criterion with the convective one.

physics.flu-dyn↗

arXiv2021

Convective, absolute and global azimuthal magnetorotational instabilities

We study the convective and absolute forms of azimuthal magnetorotational instability (AMRI) in a Taylor-Couette (TC) flow with an imposed azimuthal magnetic field. We show that the domain of the convective AMRI is wider than that of the absolute AMRI. Actually, it is the absolute instability which is the most relevant and important for magnetic TC flow experiments. The absolute AMRI, unlike the convective one, stays in the device, displaying a sustained growth that can be experimentally detected. We also study the global AMRI in a TC flow of finite height using DNS and find that its emerging butterfly-type structure -- a spatio-temporal variation in the form of upward and downward traveling waves -- is in a very good agreement with the linear stability analysis, which indicates the presence of two dominant absolute AMRI modes in the flow giving rise to this global butterfly pattern.

physics.flu-dyn↗

arXiv2020

Mode Conversion and Period Doubling at Plasma-$β$ Unity in an Alfvén-Wave Experiment with Liquid Rubidium

We report Alfvén-wave experiments with liquid rubidium at the Dresden High Magnetic Field Laboratory (HLD). Reaching up to 63 T, the pulsed magnetic field exceeds the critical value of 54 T at which the Alfvén speed becomes equal to the sound speed (plasma-$β$ unity). At this threshold we observe a period doubling of an applied 8 kHz CW excitation, a clear footprint for a parametric resonance between magnetosonic waves and Alfvén waves.

physics.plasm-ph↗

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

Numerical and Experimental Investigation of Electro-Vortex Flow in a Cylindrical Container

In a cylindrical container filled with an eutectic GaInSn alloy, an electro-vortex flow (EVF) is generated by the interaction of a non-uniform current with its own magnetic field. In this paper, we investigate the EVF phenomenon numerically and experimentally. Ultrasound Doppler Velocimetry (UDV) is applied to measure the velocity field in a cylindrical vessel. Second, we enhance an old numerical solver by taking into account the effect of Joule heating, and employ it for the numerical simulation of the EVF experiment. Special focus is laid on the role of the magnetic field, which is the combination of the current induced magnetic field and the external geomagnetic field. For getting a higher computational efficiency, the so-called parent-child mesh technique is applied in OpenFOAM when computing the electric potential, the current density and the temperature in the coupled solid-liquid conductor system. The results of the experiment are in good agreement with those of the simulation. This study may help to identify the factors that are essential for the EVF phenomenon, and for quantifying its role in liquid metal batteries.

physics.flu-dyn↗

arXiv2019

Two types of axisymmetric helical magnetorotational instability in rotating flows with positive shear

We reveal and investigate a new type of linear axisymmetric helical magnetorotational instability which is capable of destabilizing viscous and resistive rotational flows with radially increasing angular velocity, or positive shear. This instability is double-diffusive by nature and is different from the more familiar helical magnetorotational instability, operating at positive shear above the Liu limit, in that it works instead for a wide range of the positive shear when ${\rm (i)}$ a combination of axial/poloidal and azimuthal/toroidal magnetic fields is applied and ${\rm (ii)}$ the magnetic Prandtl number is not too close to unity. We study this instability first with radially local WKB analysis and then confirm its existence using a global stability analysis of the magnetized flow between two rotating cylinders with conducting or insulating boundaries. From an experimental point of view, we also demonstrate the presence of the new instability in a magnetized viscous and resistive Taylor-Couette flow with positive shear for such values of the flow parameters, which can be realized in upcoming experiments at the DRESDYN facility. Finally, this instability might have implications for the dynamics of the equatorial parts of the solar tachocline and dynamo action there, since the above two necessary conditions for the instability to take place are satisfied in this region. Our global stability calculations for the tachocline-like configuration, representing a thin rotating cylindrical layer with the appropriate boundary conditions -- conducting inner and insulating outer cylinders -- and the values of the flow parameters, indicate that it can indeed arise in this case with a characteristic growth time comparable to the solar cycle period.

physics.flu-dyn↗

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↗

arXiv2019

Length measurement and stabilisation of the diagonals of a square area laser gyroscope

Large frame ring laser gyroscopes are top sensitivity inertial sensors able to measure absolute angular rotation rate below $\rm \mathbf{prad/s}$ in few seconds. The development of ring laser based on a simple mechanical structure, usually called hetero lithic structure, requires to control the geometry of the apparatus. Our prototype GP2 is a middle size ring laser, whose main purpose is the geometry control with opto-mechanical means. The first tests have been performed, and the data analysed. The lengths of the diagonals of the ring cavity have been measured with $\pmb{μ{\rm m}}$ accuracy, and continuous operation has been obtained, without loss of sensitivity. GP2 is located in a standard laboratory, with a temperature stabilisation around 1 degree Celsius. The analysis shows that middle size ring lasers can obtain nrad/s sensitivity also in a standard environment.

physics.ins-det↗

arXiv2018

Analysis of 90 days operation of the gyroscope GINGERINO

GINGERINO is a square ring-laser prototype, which has been built to investigate the level of noise inside the Gran Sasso underground laboratory. It Is meant for fundamental physics, but it provides suitable data for geophysics and seismology. Since May 2017 it is continuously acquiring data. The analysis of the first $90$ days shows that the duty cycle is higher than $95\%$, and the quantum shot noise limit is of the order of $ 10^{-10}(\mathrm{rad}/s)/\sqrt{\mathrm{Hz}}$. It is located in a seismically active area, and it recorded part of the of central Italy earthquakes. Its high sensitivity in the frequency band of fraction of Hz makes it suitable for seismology studies. The main purpose of the present analysis is to investigate the long term response of the apparatus. Simple and fast routines to eliminate the disturbances coming from the laser have been developed. The Allan deviation of the raw data reaches $10^{-7}$ after about $10^6s$ of integration time, while the processed data shows an improvement of one order of magnitude. Disturbances at the daily time scale are present in the processed data and the expected signal induced by polar motion and solid Earth tide is covered by those disturbances.

physics.ins-det↗

arXiv2018

Laboratory experiments on dynamo action and magnetically triggered flow instabilities

Magnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilizing rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarize the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler-Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear.

physics.flu-dyn↗

arXiv2018

Self-excitation in a helical liquid metal flow: The Riga dynamo experiments

The homogeneous dynamo effect is at the root of magnetic field generation in cosmic bodies, including planets, stars and galaxies. While the underlying theory had increasingly flourished since the middle of the 20th century, hydromagnetic dynamos were not realized in laboratory until 1999. On 11 November 1999, this situation changed with the first observation of a kinematic dynamo in the Riga experiment. Since that time, a series of experimental campaigns has provided a wealth of data on the kinematic and the saturated regime. This paper is intended to give a comprehensive survey about these experiments, to summarize their main results and to compare them with numerical simulations.

physics.flu-dyn↗

arXiv2017

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI) -- a relative of the standard MRI -- in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that HMRI turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

physics.flu-dyn↗

arXiv2017

Nonmodal analysis of helical and azimuthal magnetorotational instabilities

Helical and azimuthal magnetorotational instabilities operate in rotating magnetized flows with relatively steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear, which determine the threshold of modal growth of these instabilities, are continuously connected when some axial electrical current is allowed to pass through the rotating fluid. We investigate the nonmodal dynamics of these instabilities arising from the non-normality of shear flow in the local approximation, generalizing the results of the modal approach. It is demonstrated that moderate transient/nonmodal amplification of both types of magnetorotational instability occurs within the Liu limits, where the system is stable according to modal analysis. We show that for the helical magnetorotational instability this magnetohydrodynamic behavior is closely connected with the nonmodal growth of the underlying purely hydrodynamic problem.

physics.plasm-ph↗

arXiv2017

First international comparison of fountain primary frequency standards via a long distance optical fiber link

We report on the first comparison of distant caesium fountain primary frequency standards (PFSs) via an optical fiber link. The 1415 km long optical link connects two PFSs at LNE-SYRTE (Laboratoire National de métrologie et d'Essais - SYstème de Références Temps-Espace) in Paris (France) with two at PTB (Physikalisch-Technische Bundesanstalt) in Braunschweig (Germany). For a long time, these PFSs have been major contributors to accuracy of the International Atomic Time (TAI), with stated accuracies of around $3\times 10^{-16}$. They have also been the references for a number of absolute measurements of clock transition frequencies in various optical frequency standards in view of a future redefinition of the second. The phase coherent optical frequency transfer via a stabilized telecom fiber link enables far better resolution than any other means of frequency transfer based on satellite links. The agreement for each pair of distant fountains compared is well within the combined uncertainty of a few 10$^{-16}$ for all the comparisons, which fully supports the stated PFSs' uncertainties. The comparison also includes a rubidium fountain frequency standard participating in the steering of TAI and enables a new absolute determination of the $^{87}$Rb ground state hyperfine transition frequency with an uncertainty of $3.1\times 10^{-16}$. This paper is dedicated to the memory of André Clairon, who passed away on the 24$^{th}$ of December 2015, for his pioneering and long-lasting efforts in atomic fountains. He also pioneered optical links from as early as 1997.

physics.atom-ph↗