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

One-winged butterflies: mode selection for azimuthal magnetorotational instability by thermal convection

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 Mechanic

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

Magnetic field dynamos and magnetically triggered flow instabilities

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

Dynamic transitions of the magnetized spherical Couette flow between its base state and the return flow instability

Abstract The transition between the stable base state of the magnetized spherical Couette (MSC) flow and the return flow instability is experimentally investigated. The experiments are conducted using an MSC setup consisting of insulating spheres with the ratio of the inner to the outer radii r i/r o = 0.5, Reynolds number Re = 1000 and Hartmann number Ha ∈ [25, 29]. The transition is characterized by changes in the power spectra of the azimuthal modes in the flow as Ha is dynamically changed. The transition occurs in the interval Ha ∈ [26.5, 27.5]. The evolution of the power spectra of the azimuthal modes exhibits hysteretic effect depending on whether Ha is increased or decreased within the experimental interval. The power spectra in the azimuthal modes m ∈ {3, 4} increases and remains dominant as Ha is increased, while the power spectra in m ∈ {2, 4} are dominant while the flow is time dependent due to return flow instability as Ha is decreased.</jats:p