Boundary-integral method for poloidal axisymmetric AC magnetic fields

This paper presents a boundary-integral equation (BIE) method for the calculation of poloidal axisymmetric magnetic fields applicable in a wide range of ac frequencies. The method is based on the vector potential formulation and it uses the Green's functions of Laplace and Helmholtz equations for the exterior and interior of conductors, respectively. The work is particularly focused on a calculation of axisymmetric Green's function for the Helmholtz equation which is both simpler and more accurate compared to previous approaches. Three different approaches are used for calculation of the Green's function depending on the parameter range. For low and high dimensionless ac frequencies we use a power series expansion in terms of elliptical integrals and an asymptotic series in terms of modified Bessel functions of second kind, respectively. For the intermediate frequency range, Gauss-Chebyshev-Lobatto quadratures are used. The method is verified by comparing with the analytical solution for a sphere in a uniform external ac field. The application of the method is demonstrated for a composite model inductor containing an external secondary circuit.Comment: 8 pages, 4 figure

Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct

We analyse numerically the linear stability of a liquid metal flow in a rectangular duct with perfectly electrically conducting walls subject to a uniform transverse magnetic field. A non-standard three dimensional vector stream function/vorticity formulation is used with Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. A relatively weak magnetic field is found to render the flow linearly unstable as two weak jets appear close to the centre of the duct at the Hartmann number Ha \approx 9.6. In a sufficiently strong magnetic field, the instability following the jets becomes confined in the layers of characteristic thickness \delta \sim Ha^{-1/2} located at the walls parallel to the magnetic field. In this case the instability is determined by \delta, which results in both the critical Reynolds and wavenumbers numbers scaling as \sim \delta^{-1}. Instability modes can have one of the four different symmetry combinations along and across the magnetic field. The most unstable is a pair of modes with an even distribution of vorticity along the magnetic field. These two modes represent strongly non-uniform vortices aligned with the magnetic field, which rotate either in the same or opposite senses across the magnetic field. The former enhance while the latter weaken one another provided that the magnetic field is not too strong or the walls parallel to the field are not too far apart. In a strong magnetic field, when the vortices at the opposite walls are well separated by the core flow, the critical Reynolds and wavenumbers for both of these instability modes are the same: Re_c \approx 642Ha^{1/2}+8.9x10^3Ha^{-1/2} and k_c \approx 0.477Ha^{1/2}. The other pair of modes, which differs from the previous one by an odd distribution of vorticity along the magnetic field, is more stable with approximately four times higher critical Reynolds number.Comment: 16 pages, 8 figures, revised version, to appear in J. Fluid Mec

Contactless Electromagnetic Phase-Shift Flowmeter for Liquid Metals

We present a concept and test results of an eddy-current flowmeter for liquid metals. The flow rate is determined by applying a weak ac magnetic field to a liquid metal flow and measuring the flow-induced phase disturbance in the external electromagnetic field. The phase disturbance is found to be more robust than that of the amplitude used in conventional eddy-current flowmeters. The basic characteristics of this type of flowmeter are analysed using simple theoretical models, where the flow is approximated by a solid body motion. Design of such a flowmeter is presented and its test results reported.Comment: 19 pages, 13 figures, to appear in Meas. Sci. Technol (final version

Cameras and carcasses: historical and current methods for using artificial food falls to study deep-water animals

Deep-ocean animals remain poorly understood compared to their shallow-water relatives, mainly because of the great cost and difficulty involved in obtaining reliable ecological data. This is a serious issue as exploitation of deep-water resources progresses without sufficient data being available to assess its risks and impacts. First described almost 40 years ago, the use of baited cameras was pioneered by deep-sea biologists and is now a widely used technique for the assessing patterns of animal behaviour, abundance and biodiversity. The technique provides a non-destructive and cost-effective means of collecting data, where other techniques such as trawling are difficult or impractical. This review will first describe the evolution of baited camera techniques in deep-sea research from the early deployments, through recent programs to investigate trends in animal distribution with depth, latitude, and ocean basin. In the second section the techniques used for imaging, baiting, and analysis are synthesized, with special consideration for the modeling techniques used in assessing animal abundance and biomass

Bathyal demersal fishes of the Charlie-Gibbs Fracture Zone region (49°–54°N) of the Mid-Atlantic Ridge : III. Results from remotely operated vehicle (ROV) video transects

Peer reviewedPublisher PD

Elementary model of internal electromagnetic pinch-type instability

We analyse numerically a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. Our model is as simple as possible but still captures the salient features of the instability which otherwise may be obscured by the technical details of more comprehensive numerical models and laboratory experiments. Firstly, we show the instability in liquid metals, which are relatively poor conductors, differs significantly from the astrophysically-relevant Tayler instability. In liquid metals, the instability develops on the magnetic response time scale, which depends on the conductivity and is much longer than the Alfv\'en time scale, on which the Tayler instability develops in well conducting fluids. Secondly, we show that this instability is an edge effect caused by the curvature of the magnetic field, and its growth rate is determined by the linear current density and independent of the system size. Our results suggest that this instability may affect future liquid metal batteries when their size reaches a few meters.Comment: 14 pages, 5 figures (to appear in J Fluid Mech