Bernard Knaepen

Theory of the Lorentz force flowmeter

A Lorentz force flowmeter is a device for the contactless measurement of flow rates in electrically conducting fluids. It is based on the measurement of a force on a magnet system that acts upon the flow. We formulate the theory of the Lorentz force flowmeter which connects the measured force to the unknown flow rate. We first apply the theory to three specific cases, namely (i) pipe flow exposed to a longitudinal magnetic field, (ii) pipe flow under the influence of a transverse magnetic field and (iii) interaction of a localized distribution of magnetic material with a uniformly moving sheet of metal. These examples provide the key scaling laws of the method and illustrate how the force depends on the shape of the velocity profile and the presence of turbulent fluctuations in the flow. Moreover, we formulate the general kinematic theory which holds for arbitrary distributions of magnetic material or electric currents and for any velocity distribution and which provides a rational framework for the prediction of the sensitivity of Lorentz force flowmeters in laboratory experiments and in industrial practice.

Thermal Conduction in Magnetized Turbulent Gas

Using numerical methods, we systematically study in the framework of ideal MHD the effect of magnetic fields on heat transfer within a turbulent gas. We measure the rates of passive scalar diffusion within magnetized fluids and make the comparisons (1) between MHD and hydrodynamic simulations, (2) between different MHD runs with different values of the external magnetic field (up to the energy equipartition value), and (3) between thermal conductivities parallel and perpendicular to the magnetic field. We do not find apparent suppression of diffusion rates by the presence of magnetic fields, which implies that magnetic fields do not suppress heat diffusion by turbulent motions.

All consistent interactions for exterior form gauge fields

We give the complete list of all first-order consistent interaction vertices for a set of exterior form gauge fields of form degree {gt}1, described in the free limit by the standard Maxwell-like action. Special attention is paid to the interactions that deform the gauge transformations. These are shown to be necessarily of the Noether form {open_quotes}conserved antisymmetric tensor{close_quotes} times {open_quotes}p-form potential{close_quotes} and exist only in particular spacetime dimensions. Conditions for consistency to all orders in the coupling constant are given. For illustrative purposes, the analysis is carried out explicitly for a system of forms with two different degrees p and q (1{lt}p{lt}q{lt}n). {copyright} {ital 1997} {ital The American Physical Society}

Energy transfers in forced MHD turbulence

The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsässer variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.

Large-eddy simulation of conductive flows at low magnetic reynolds number

Using the method of large-eddy simulation, we study decaying homogeneous turbulence of a conductive flow under the influence of an applied external magnetic field at low magnetic Reynolds number. In order to assess the performance of large-eddy simulation, comparison with high resolution (512 3 ) direct numerical simulation is performed. Results show that the modeling of subgrid scales using the dynamic Smagorinsky model is very effective in the present context.

Large eddy simulation of decaying magnetohydrodynamic turbulence with dynamic subgrid-modeling

The numerical large eddy simulation (LES) technique is tested on decaying magnetohydrodynamic (MHD) turbulence. The LES approach allows for a strong reduction in computational cost compared to direct numerical simulations by modeling the effects of the smallest turbulent scales instead of computing them directly. Two small-scale models of eddy-viscosity type are presented for this purpose in combination with a procedure for the self-consistent calculation of the model parameters in the course of the simulation. The method is successfully tested by comparing the obtained results to a high-resolution direct numerical simulation of decaying three-dimensional MHD turbulence.

Magnetohydrodynamic turbulence at moderate magnetic Reynolds number

We consider the case of homogeneous turbulence in a conducting fluid that is exposed to a uniform external magnetic field at low to moderate magnetic Reynolds numbers (by moderate we mean here values as high as 20). When the magnetic Reynolds number is vanishingly small (

Characteristic cohomology of p-form gauge theories

R_m \ll 1

The transport of a passive scalar in magnetohydrodynamic turbulence subjected to mean shear and frame rotation

), it is customary to simplify the governing magnetohydrodynamic (MHD) equations using what is known as the quasi-static (QS) approximation. As the magnetic Reynolds number is increased, a progressive transition between the physics described by the QS approximation and the MHD equations occurs. We show here that this intermediate regime can be described by another approximation which we call the quasi-linear (QL) approximation. For the numerical simulations performed, the predictions of the QL approximation are in good agreement with those of MHD for magnetic Reynolds number up to

Anisotropy of velocity spectra in quasistatic magnetohydrodynamic turbulence

R_m \sim 20