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In this paper, we present numerical and experimental results on helicity oscillations in a liquid-metal Rayleigh-B\'enard (RB) convection cell, with an aspect ratio of 0.5. We find that helicity oscillations occur during transitions of flow states that are characterised by significant changes in the Reynolds number. Moreover, we also observe helicity oscillations at flow conditions where the temporal gradient of the change in the Reynolds number is significantly smaller than that of the helicity. Notably, the helicity oscillations observed during the transient double-roll state exhibit characteristics remarkably similar to those associated with the Tayler Instability., Comment: 10 pages, 16 figures

The effects of thermal convection on turbulence in accretion discs, and particularly its interplay with the magnetorotational instability (MRI), are of significant astrophysical interest. Despite extensive theoretical and numerical studies, such an interplay has not been explored experimentally. We conduct linear analysis of the azimuthal version of MRI (AMRI) in the presence of thermal convection and compare the results with our experimental data published before. We show that the critical Hartmann number ($Ha$) for the onset of AMRI is reduced by convection. Importantly, convection breaks symmetry between $m = \pm 1$ instability modes ($m$ is the azimuthal wavenumber). This preference for one mode over the other makes the AMRI-wave appear as a ``one-winged butterfly''., Comment: 11 pages, 5 figures, accepted for publication in the Journal of Fluid Mechanics

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 Poincar\'{e} 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., Comment: 9 pages, 5 figures, accepted for publication in Physical Review E

We propose a self-consistent explanation of Rieger-type periodicities, the Schwabe cycle, and the Suess-de Vries cycle of the solar dynamo in terms of resonances of various wave phenomena with gravitational forces exerted by the orbiting planets. Starting on the high-frequency side, we show that the two-planet spring tides of Venus, Earth and Jupiter are able to excite magneto-Rossby waves which can be linked with typical Rieger-type periods. We argue then that the 11.07-year beat period of those magneto-Rossby waves synchronizes an underlying conventional $\alpha-\Omega$-dynamo, by periodically changing either the field storage capacity in the tachocline or some portion of the $\alpha$-effect therein. We also strengthen the argument that the Suess-de Vries cycle appears as an 193-year beat period between the 22.14-year Hale cycle and a spin-orbit coupling effect related with the 19.86-year rosette-like motion of the Sun around the barycenter., Comment: 32 pages, 13 figures

The quest for an unambiguous detection of magnetorotational instability (MRI) in experiments is still ongoing despite recent promising results. To conclusively identify MRI in the laboratory, a large cylindrical Taylor-Couette experiment with liquid sodium is under construction within the DRESDYN project. In this paper, we investigate the linear and nonlinear dynamics of non-axisymmetric MRI in the magnetized Taylor-Couette flow of liquid sodium, which is a model flow in this experiment. We show that the achievable highest Lundquist $Lu = 10$ and magnetic Reynolds $Rm = 40$ numbers in this experiment are large enough for the linear instability of non-axisymmetric modes with azimuthal wavenumber $|m|=1$, although the corresponding critical values of these numbers are usually higher than those for the axisymmetric mode. The structure of the ensuing nonlinear saturated state and its scaling properties with respect to Reynolds number $Re$ are analyzed, which are important for the DRESDYN-MRI experiment having very high $Re \gtrsim 10^6$. It is shown that for $Re \lesssim 4\times 10^4$, the non-axisymmetric MRI modes eventually decay, since the modified shear profile of the mean azimuthal velocity due to the nonlinear axisymmetric MRI appears to be stable against non-axisymmetric instabilities. By contrast, for larger $Re \gtrsim 4\times 10^4$, a rapid growth and saturation of the non-axisymmetric modes of nonmagnetic origin occurs, which are radially localized near the inner cylinder wall, forming a turbulent boundary layer. However, for all the parameters considered, the saturation amplitude of these non-axisymmetric modes is always a few orders smaller than that of the axisymmetric MRI mode. Therefore, the results of our previous axisymmetric study on the scaling properties of nonlinear MRI states also hold when non-axisymmetric modes are included., Comment: 19 pages, 20 figures, 2 Tables, accepted for publication in Physical Review Fluids

Context: The old question of whether the solar dynamo is synchronized by the tidal forces of the orbiting planets has recently received renewed interest, both from the viewpoint of historical data analysis and in terms of theoretical and numerical modelling. Aims: We aim to contribute to the solution of this longstanding puzzle by analyzing cosmogenic radionuclide data from the last millennium. Methods: We reconsider a recent time-series of $^{14}$C-inferred sunspot data and compare the resulting cycle minima and maxima with the corresponding conventional series down to 1610 A.D., enhanced by Schove's data before that time. Results: We find that, despite recent claims to the contrary, the $^{14}$C-inferred sunspot data are well compatible with a synchronized solar dynamo, exhibiting a relatively phase-stable period of 11.07 years, which points to a synchronizing role of the spring tides of the Venus-Earth-Jupiter system., Comment: 8 pages, 7 figures

Magnetic fields are key ingredients for heating the solar corona to temperatures of several million Kelvin. A particularly important region with respect to this is the so-called magnetic canopy below the corona, where sound and Alfv\'en waves have roughly the same speed and can, therefore, easily transform into each other. We present the results of an Alfv\'en-wave experiment with liquid rubidium carried out in a pulsed field of up to 63 T. At the critical point of 54 T, where the speeds of Alfv\'en waves and sound coincide, a new 4 kHz signal appears in addition to the externally excited 8 kHz torsional wave. This emergence of an Alfv\'en wave with a doubled period is in agreement with the theoretical predictions of a parametric resonance between the two wave types. We also present preliminary results from numerical simulations of Alfv\'en and magneto-sonic waves using a compressible MHD code., Comment: 7 pages, 4 figures

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., Comment: 8 pages, 5 figures

We consider a conventional $\alpha-\Omega$-dynamo model with meridional circulation that exhibits typical features of the solar dynamo, including a Hale cycle period of around 20 years and a reasonable shape of the butterfly diagram. With regard to recent ideas of a tidal synchronization of the solar cycle, we complement this model by an additional time-periodic $\alpha$-term that is localized in the tachocline region. It is shown that amplitudes of some dm/s are sufficient for this $\alpha$-term to become capable of entraining the underlying dynamo. We argue that such amplitudes of $\alpha$ may indeed be realistic, since velocities in the range of m/s are reachable, e.g., for tidally excited magneto-Rossby waves., Comment: 14 pages, 6 figures

Magnetorotational instability (MRI) is the most likely mechanism driving angular momentum transport in astrophysical disks. However, despite many efforts, a conclusive experimental evidence of MRI is still missing. Recently, performing 1D linear analysis of the standard MRI (SMRI) in a cylindrical Taylor-Couette (TC) flow with an axial magnetic field, we showed that SMRI can be detected in the upcoming DRESDYN-MRI experiment based on a magnetized TC flow of liquid sodium. In this study, also related to DRESDYN-MRI experiments, we focused on the nonlinear evolution and saturation properties of SMRI and analyzed its scaling behavior with respect to the main parameters of the TC flow. We did a detailed analysis over the extensive ranges of magnetic Reynolds number $Rm\in [8.5, 37.1]$, Lundquist number $Lu\in[1.5, 15.5]$ and Reynolds number, $Re\in[10^3, 10^5]$. We considered small magnetic Prandtl numbers, $Pm \ll 1$, down to $Pm\sim 10^{-4}$, aiming at values typical of liquid sodium in the experiments. In the saturated state, the magnetic energy of SMRI and torque due to perturbations on the cylinders, which characterizes angular momentum transport, both increase with $Rm$ for fixed $(Lu, Re)$, while for fixed $(Lu, Rm)$, the magnetic energy decreases and torque increases with increasing $Re$. We studied the scaling of the magnetic energy and torque in the saturated state as a function of $Re$ and find a power law dependence $Re^{-0.6...-0.5}$ for the magnetic energy and $Re^{0.4...0.5}$ for the torque at all $(Lu, Rm)$ and high $Re\geq 4000$. We also explored the dependence on Lundquist number and angular velocity of the cylinders. These scaling laws will be instrumental in the subsequent analysis of more realistic finite-length TC flows and comparison of numerical results with those obtained from the DRESDYN-MRI experiments to unambiguously identify SMRI in laboratory., Comment: 22 pages, 18 figures, 2 Tables, accepted for publication in Physical Review Fluids

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., Comment: 20 pages, 16 figures, 1 table, submitted to Physics of Fluids

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-B\'enard 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., Comment: 6 pages, 7 figures

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 (Poincar\'{e}), Kelvin, Alfv\'{e}n 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 $\beta$-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., Comment: 29 pages, 14 figures

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 (Poincar\'e number), and the accompanying transition between a laminar and turbulent flow. Compared to the reference case with a 90{\deg} nutation angle, prograde rotation leads to an earlier breakdown, while in the retrograde case the forced mode continues to exist also for higher Poincar\'e 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 Poincar\'e number. Optimal dynamo conditions are found for 90{\deg} angle which, however, might shift to slightly retrograde precession for higher Reynolds numbers., Comment: 9 pages, 8 figures

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., Comment: 18 pages, 13 figures, accepted for publication in Physical Review Fluids

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., Comment: 11 pages, 6 figures, accepted for publication in J. Fluid Mech. Rapids

We report Alfv\'en-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 Alfv\'en speed becomes equal to the sound speed (plasma-$\beta$ 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 Alfv\'en waves., Comment: 5 pages, 4 figures

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., Comment: 14 pages, 16 figures; to be published in Astronomische Nachrichten

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., Comment: 16 pages, 8 figures

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., Comment: 11 pages, 4 figures, final version as published

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., Comment: Contains 3 tables and 8 figures. Published in the Journal of Nonlinear Science

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 $\pmb{\mu {\rm m}}$ 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., Comment: 4 pages, 5 figures

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., Comment: 15 pages, 13 figures, accepted for publication in Phys. Rev. Fluids

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., Comment: 15 pages, 12 figures

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., Comment: 21 pages, 7 figures

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., Comment: 20 pages, 16 figures

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., Comment: 26 pages, 9 figures, accepted for publication in New Journal of Physics

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 m\'{e}trologie et d'Essais - SYst\`{e}me de R\'{e}f\'{e}rences 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 Andr\'{e} 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.

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., Comment: 10 pages, 4 figures, extended proceedings paper for the PAMIR 2016 conference

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 some smaller liquid metal experiments devoted to various magnetic instabilities such as the helical and the azimuthal magnetorotational instability, the Tayler instability, and the different instabilities that appear in a magnetized spherical Couette flow. We conclude with an outlook on a large scale Tayler-Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear., Comment: 27 pages, 11 figures

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., Comment: 10 pages, 4 figures, extended proceedings paper of the PAMIR 2016 conference

First results of a new spherical Couette experiment are presented. The liquid metal flow in a spherical shell is exposed to a homogeneous axial magnetic field. For a Reynolds number Re=1000, we study the effect of increasing Hartmann number Ha. The resulting flow structures are inspected by ultrasound Doppler velocimetry. With a weak applied magnetic field, we observe an equatorially anti-symmetric jet instability with azimuthal wave number m=3. As the magnetic field strength increases, this instability vanishes. When the field is increased further, an equatorially symmetric return flow instability arises. Our observations are shown to be in good agreement with linear stability analysis and non-linear flow simulations., Comment: 10 pages, 6 figures, submitted to Magnetohydrodynamics

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., Comment: 18 pages, 7 figures, accepted by Solar Physics

Leveraging the unrivaled performance of optical clocks in applications in fundamental physics beyond the standard model, in geo-sciences, and in astronomy requires comparing the frequency of distant optical clocks truthfully. Meeting this requirement, we report on the first comparison and agreement of fully independent optical clocks separated by 700 km being only limited by the uncertainties of the clocks themselves. This is achieved by a phase-coherent optical frequency transfer via a 1415 km long telecom fiber link that enables substantially better precision than classical means of frequency transfer. The fractional precision in comparing the optical clocks of three parts in $10^{17}$ was reached after only 1000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than with any other existing frequency transfer method. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second., Comment: 14 pages, 3 figures, 1 table

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 ${\rm{Po}}=\Omega_p/\Omega_c=0.014$ 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., Comment: 26 pages, 14 figures, submitted to New J. Phys

It is known that in a hydrodynamic Taylor-Couette system uniform rotation or a rotation law with positive shear ('super-rotation') are linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong axial electric-current becomes unstable against nonaxisymmetric disturbances. It is thus suggestive that a cylindric pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with $d\Omega/dR \geq 0$. However, for magnetic Prandtl numbers Pm$\neq 1$ and for slow rotation also rigid rotation and super-rotation support the instability by lowering their critical Hartmann numbers. For super-rotation in narrow gaps and for modest rotation rates this double-diffusive instability even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile $B_\phi\propto 1/R$ included. For rigid rotation and for super-rotation the sign of the azimuthal drift of the nonaxisymmetric hydromagnetic instability pattern strongly depends on the magnetic Prandtl number. The pattern counterrotates with the flow for Pm$\ll 1$ and it corotates for Pm$\gg 1$ while for rotation laws with negative shear the instability pattern migrates in the direction of the basic rotation for all Pm. An axial electric-current of minimal 3.6 kAmp flowing inside or outside the inner cylinder suffices to realize the double-diffusive instability for super-rotation in experiments using liquid sodium as the conducting fluid between the rotating cylinders. The limit is 11 kAmp if a gallium alloy is used., Comment: 17 pages, 9 figures, submitted to PoF

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., Comment: 9 pages, 9 figures, accepted for Magnetohydrodynamics (PAMIR 2014 special issue)

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., Comment: 9 pages, 6 figures, submitted to Magnetohydrodynamics

The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be also a limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries. Particular focus is laid on the detailed influence of the axial electrical boundary conditions on the characteristic features of the Tayler instability, and, secondly, on the occurrence of electro-vortex flows and their relevance for liquid metal batteries., Comment: 26 pages, 16 figures