43 research outputs found
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
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
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
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
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
Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field
The effect of a homogeneous magnetic field on surface-tension-driven
B\'{e}nard convection is studied by means of direct numerical simulations. The
flow is computed in a rectangular domain with periodic horizontal boundary
conditions and the free-slip condition on the bottom wall using a
pseudospectral Fourier-Chebyshev discretization. Deformations of the free
surface are neglected. Two- and three-dimensional flows are computed for either
vanishing or small Prandtl number, which are typical of liquid metals. The main
focus of the paper is on a qualitative comparison of the flow states with the
non-magnetic case, and on the effects associated with the possible
near-cancellation of the nonlinear and pressure terms in the momentum equations
for two-dimensional rolls. In the three-dimensional case, the transition from a
stationary hexagonal pattern at the onset of convection to three-dimensional
time-dependent convection is explored by a series of simulations at zero
Prandtl number.Comment: 26 pages, 9 figure