Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary conditions in order to minimize the critical magnetic Reynolds number and hence the necessary motor power. The main focus of this paper lies on the role of ''lid layers'', i.e. layers of liquid sodium between the impellers and the end walls of the cylinder. First, we study an analytical test flow to show that lid layers can have an ambivalent effect on the efficiency of the dynamo. The critical magnetic Reynolds number shows a flat minimum for a small lid layer thickness, but increases for thicker layers. For the actual VKS geometry it is shown that static lid layers yield a moderate increase of the critical magnetic Reynolds number by approximately 12 per cent. A more dramatic increase by 100 until 150 per cent can occur when some rotational flow is taken into account in those layers. Possible solutions of this problem are discussed for the real dynamo facility.Comment: 24 pages, 11 figures, minor changes, to appear in European Journal of Mechanics B/Fluid

Ondes hydrothermales non-linéaires dans un disque et un anneau

URL: http://www-spht.cea.fr/articles/S98/109Nous nous intéressons à la convection thermocapillaire, produite par l'imposition d'un gradient {\it horizontal} de température sur une mince couche de fluide avec surface libre. En géométrie bidimensionnelle nous observons deux modes différents en compétition, tandis qu'en géométrie bidimensionnelle avec conditions limites périodiques, nous étudions la transition à la turbulence d'une onde propagative homogène

Experimental evidence of a phase transition in a turbulent swirling flow

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On the properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e. a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent flow.Comment: latex prl-stationary-051215arxiv.tex, 9 files, 6 figures, 4 pages (http://www-drecam.cea.fr/spec/articles/S06/008/

Towards an experimental von Karman dynamo: numerical studies for an optimized design

Numerical studies of a kinematic dynamo based on von Karman type flows between two counterrotating disks in a finite cylinder are reported. The flow has been optimized using a water model experiment, varying the driving impellers configuration. A solution leading to dynamo action for the mean flow has been found. This solution may be achieved in VKS2, the new sodium experiment to be performed in Cadarache, France. The optimization process is described and discussed, then the effects of adding a stationary conducting layer around the flow on the threshold, on the shape of the neutral mode and on the magnetic energy balance are studied. Finally, the possible processes involved into kinematic dynamo action in a von Karman flow are reviewed and discussed. Among the possible processes we highlight the joint effect of the boundary-layer radial velocity shear and of the Ohmic dissipation localized at the flow/outer-shell boundary

Magnetic field reversals in an experimental turbulent dynamo

We report the first experimental observation of reversals of a dynamo field generated in a laboratory experiment based on a turbulent flow of liquid sodium. The magnetic field randomly switches between two symmetric solutions B and -B. We observe a hierarchy of time scales similar to the Earth's magnetic field: the duration of the steady phases is widely distributed, but is always much longer than the time needed to switch polarity. In addition to reversals we report excursions. Both coincide with minima of the mechanical power driving the flow. Small changes in the flow driving parameters also reveal a large variety of dynamo regimes.Comment: 5 pages, 4 figure

Transport of magnetic field by a turbulent flow of liquid sodium

We study the effect of a turbulent flow of liquid sodium generated in the von K\'arm\'an geometry, on the localized field of a magnet placed close to the frontier of the flow. We observe that the field can be transported by the flow on distances larger than its integral length scale. In the most turbulent configurations, the mean value of the field advected at large distance vanishes. However, the rms value of the fluctuations increases linearly with the magnetic Reynolds number. The advected field is strongly intermittent.Comment: 4 pages, 6 figure

Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].Comment: 25 pages; 16 figure

Convective and absolute Eckhaus instability leading to modulated waves in a finite box

We report experimental study of the secondary modulational instability of a one-dimensional non-linear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatio-temporal defects are linked to the convective and absolute nature of the instability. Both transitions appear to be subcritical. The spatio-temporal defects control the global mode structure.Comment: 5 pages, 7 figures (ReVTeX 4 and amsmath.sty), final versio