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Numerical models of planetary MHD dynamos have led to many advances in the last twenty years. However, the accessible parameter space of these models is somewhat limited due to computational constraints. A number of numerically based scaling laws have been proposed, but it has been difficult to reliably confirm them from the simulation data alone. Since these scaling laws have to be used to extend the numerical models into the planetary parameter regime, getting correct scalings is an important issue. Here some possible balances between the relevant terms in the dynamo equations are considered, and a number of different known and new scaling laws are proposed and justified from analytical point of view. Some of these laws are compatible with the widely known Christensen and Aubert (Geophys. J. Int. 2006, 166) scaling for the magnetic field strength. Plausible estimates of the typical values of the important quantities in the Earth's core and other Terrestrial planets are made, and the extent to which the various scaling laws are consistent with these estimates is discussed. [ABSTRACT FROM AUTHOR]

There has for many years been interest in finding necessary conditions for dynamo action. These are usually expressed in terms of bounds on integrated properties of the flow. The bounds can clearly be improved when the flow structure can be taken into account. Recent research presents techniques for finding optimised dynamos (that is with the lowest dynamo threshold) subject to constraints, (e.g. with fixed mean squarevorticity). It is natural to ask if such an optimum solution can exist when the mean squarevelocityis fixed. The aim of this note is to show that this is not the case and in fact that a steady or periodic dynamo can exist in a bounded conductor with an arbitrarily small value of the kinetic energy. [ABSTRACT FROM PUBLISHER]

The axisymmetric kinematic dynamo problem is reconsidered, and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions; i.e., we assume a compressible fluid of variable (in space and time) conductivity moving in an arbitrary (axisymmetric) domain. We prove unconditional, pointwise, and exponential decay of the magnetic field and electric current to zero. The decay rate of the external (meridional) magnetic field can become very small (compared to free decay) for special flow fields and large magnetic Reynolds numbers, as we demonstrate with an example. On the other hand, we show for fluids with weak variation of mass density and conductivity that the meridional and azimuthal decay rates do not drop significantly below those of free decay. [ABSTRACT FROM AUTHOR]

The induction equation of magnetohydrodynamics (MHD) is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD. [ABSTRACT FROM PUBLISHER]

Experimental results are reported on the magnetohydrodynamic interaction between oscillating flows in adjoining channels of the Karlsruhe dynamo test facility. In the experiment, designed to simulate the Roberts–Busse kinematic dynamo model, a time periodic perturbation has been imposed on the axial channel flows, while the flow rates in the other two helical channel systems were supplied at constant power level. It has been observed that the onset of dynamo action is shifted slightly to lower mean flow rates. A temporal analysis shows distinct correlations between the evolving magnetic field and the different kinds of forced flows in the channels. From the beginning the environmental magnetic field adjusts to fluctuations of the axial channel flow. The fluctuations of the magnetic field increase owing to dynamo action in a transition range and induce quasiperiodic fluctuations on the flow in the helical channels by acting Lorentz forces. In the high supercritical range the fluctuations are dampened. [ABSTRACT FROM AUTHOR]

A simple model of precessionally-forced flow has been proposed and studied by Mason and Kerswell (Mason, R.M. and Kerswell, R.R., Chaotic dynamics in a strained rotating flow: a precessing plane fluid layer. Geophys. Astrophys. Fluid Dynam., 491, 2002, 71-106). The fluid is viscous and incompressible and occupies a plane layer that spins about its normal that itself precesses about an axis fixed in space. The present article confirms the linear stability results of Mason and Kerswell and investigates in greater detail the complicated bifurcation that arises at the onset of two-dimensional instability. Three-dimensional modes are studied and it is shown that, if the fluid is sufficiently electrically conducting, the motions can, for sufficiently strong precessional forcing, maintain a magnetic field by dynamo action. The Lorentz force is found to reduce the vigor of the motions but to modify them in a way that assists magnetic field generation. [ABSTRACT FROM AUTHOR]

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincaré return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famous Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point. [ABSTRACT FROM AUTHOR]

The growth of magnetic field is considered in the stretch–fold–shear map in the limit of weak diffusion. Numerical results are given for insulating, perfectly conducting and periodic boundary conditions. The resulting eigenvalue branches and magnetic fields are related to eigenvalue branches for perfect dynamo action, obtained for zero diffusion using a complex variable formulation. The effect of diffusion on these perfect dynamo modes depends on their structure, growth rate and the diffusive boundary conditions employed. In some cases, the effect of diffusion is a small perturbation, giving a correction going to zero in the limit of weak diffusion, with a scaling exponent given analytically. In other cases weak diffusion can entirely destroy a perfect dynamo branch. Diffusive boundary layers can also generate entirely new branches. These different cases are elucidated, and within the framework of the asymptotic approximations used (which do not constitute a rigorous proof), it is seen that for all three boundary conditions employed, the stretch–fold–shear map is a fast dynamo. [ABSTRACT FROM AUTHOR]

A new MHD (magnetohydrodynamics) generator based on electromotive force using seawater, that is, a helical-type seawater MHD generator with a 7 T solenoid superconducting magnet, is designed, constructed and tested. The constructed generator contains a helical insulation wall made of polyvinyl chloride 140 mm long and 100 mm in diameter, an anode rod made of SUS316 1350 mm long and 10 mm in diameter, and a cathode pipe made of SUS316 260 mm long and 100 mm in diameter. In the experiment, electromotive force and generator output are measured in terms of average flow velocity (0-5.6 m/s) and magnetic field (0-7 T) using artificial seawater (3.4% NaCl aqueous solution). As a result of the experiment, it was found that the electromotive force increases proportionally to average flow velocity and magnetic field, and that the generator output increases quadratically to average flow velocity and magnetic field over certain points. Experimental values are discussed by comparing the theoretical values and computed values. [ABSTRACT FROM AUTHOR]