The magnetorotational instability (MRI) is thought to play a key role in the formation of stars and black holes by sustaining the turbulence in hydrodynamically stable Keplerian accretion disks. In previous experiments the MRI was observed in a liquid metal Taylor-Couette flow at moderate Reynolds numbers by applying a helical magnetic field. The observation of this helical MRI (HMRI) was interfered with a significant Ekman pumping driven by solid end caps that confined the instability only to a part of the Taylor-Couette cell. This paper describes the observation of the HMRI in an improved Taylor-Couette setup with the Ekman pumping significantly reduced by using split end caps. The HMRI, which now spreads over the whole height of the cell, appears much sharper and in better agreement with numerical predictions. By analyzing various parameter dependencies we conclude that the observed HMRI represents a self-sustained global instability rather than a noise-sustained convective one.

We analyse numerically the linear stability of the fully developed flow of a liquid metal in a rectangular duct subject to a transverse magnetic field. The walls of the duct perpendicular to the magnetic field are perfectly conducting whereas the parallel ones are insulating. In a sufficiently strong magnetic field, the flow consists of two jets at the insulating walls and a near-stagnant core. We use a vector stream function formulation and Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. Due to the two-fold reflection symmetry of the base flow the disturbances with four different parity combinations over the duct cross-section decouple from each other. Magnetic field renders the flow in a square duct linearly unstable at the Hartmann number Ha 5.7 with respect to a disturbance whose vorticity component along the magnetic field is even across the field and odd along it. For this mode, the minimum of the critical Reynolds number Re_c 2018, based on the maximal velocity, is attained at Ha ~ 10. Further increase of the magnetic field stabilises this mode with Re_c growing approximately as Ha. For Ha>40, the spanwise parity of the most dangerous disturbance reverses across the magnetic field. At Ha ~ 46 a new pair of most dangerous disturbances appears with the parity along the magnetic field being opposite to that of the previous two modes. The critical Reynolds number, which is very close for both of these modes, attains a minimum Re_c ~ 1130 at Ha ~ 70 and increases as Re_c ~ Ha^1/2 for Ha >> 1. The asymptotics of the critical wavenumber is k_c ~ 0.525Ha^1/2 while the critical phase velocity approaches 0.475 of the maximum jet velocity.Comment: 20 pages, 13 figures, production version, to appear in J. Fluid Mec

We consider the magnetorotational instability (MRI) of a hydrodynamically stable Taylor-Couette flow with a helical external magnetic field in the inductionless approximation defined by a zero magnetic Prandtl number (Pm=0) . This leads to a considerable simplification of the problem eventually containing only hydrodynamic variables. First, we point out that magnetic field adds more dissipation while it does not change the base flow which is the only source of energy for growing perturbations. Thus, it seems unclear from the energetic point of view how such a hydrodynamically stable flow can turn unstable in the presence of a helical magnetic field as it has been found recently by Hollerbach and Rüdiger [Phys. Rev. Lett. 95, 124501 (2005)]. We revisit this problem by using a Chebyshev collocation method to calculate the eigenvalue spectrum of the linearized problem. In this way, we confirm that a helical magnetic field can indeed destabilize the flow in the inductionless approximation. Second, we integrate the linearized equations in time to study the transient behavior of small amplitude perturbations, thus showing that the energy arguments are correct as well. However, there is no real contradiction between both facts. The linear stability theory predicts the asymptotic development of an arbitrary small-amplitude perturbation, while the energy stability theory yields the instant growth rate of any particular perturbation, but it does not account for the evolution of this perturbation. Thus, although switching on the magnetic field instantly increases the energy decay rate of the dominating hydrodynamic perturbation, in the same time this perturbation ceases to be an eigenmode in the presence of the magnetic field. Consequently, this perturbation is transformed with time and so becomes able to extract energy from the base flow necessary for the growth.

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.

We present a theory of single-magnet flowmeter for liquid metals and compare it with experimental results. The flowmeter consists of a freely rotating permanent magnet, which is magnetized perpendicularly to the axle it is mounted on. When such a magnet is placed close to a tube carrying liquid metal flow, it rotates so that the driving torque due to the eddy currents induced by the flow is balanced by the braking torque induced by the rotation itself. The equilibrium rotation rate, which varies directly with the flow velocity and inversely with the distance between the magnet and the layer, is affected neither by the electrical conductivity of the metal nor by the magnet strength. We obtain simple analytical solutions for the force and torque on slowly moving and rotating magnets due to eddy currents in a layer of infinite horizontal extent. The predicted equilibrium rotation rates qualitatively agree with the magnet rotation rate measured on a liquid sodium flow in stainless steel duct.Comment: 15 pages, 6 figures, revised version, to appear in J. Appl. Phy