Romain Monchaux

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

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 Earths 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.

Preferential concentration of heavy particles: A Voronoï analysis

We present an experimental characterization of preferential concentration and clustering of inertial particles in a turbulent flow obtained from Voronoi diagram analysis. Several results formerly obtained from various data processing techniques are successfully recovered and further analyzed with Voronoi tesselations as the main single tool. We introduce a simple and nonambiguous way to identify particle clusters. We emphasize the maximum preferential concentration for particles with Stokes numbers around unity and the self-similar nature of clustering and we report new unpredicted results concerning clusters inner concentration dependence on Stokes number and global seeding density. Some of these experimental observations can be consistently interpreted in the context of the so-called sweep-stick mechanism. Finally, we stress the great potential of Voronoi analysis that offers important openings for new investigations of particle laden flows in terms, for instance, of simultaneous Lagrangian statistics of particle dynamics and local concentration field.

The von Karman Sodium experiment: Turbulent dynamical dynamos

The von Karman Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Karman geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is R-pi-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

Properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von Kármán 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 nonhomogeneous nonisotropic turbulent flow.

Normalized kinetic energy as a hydrodynamical global quantity for inhomogeneous anisotropic turbulence

We introduce a hydrodynamical global quantity δ that characterizes turbulent fluctuations in inhomogeneous anisotropic flows. This time dependent quantity is constructed as the ratio of the instantaneous kinetic energy of the flow to the kinetic energy of the time-averaged flow. Such a normalization based on the dynamics of the flow makes this quantity comparable from one turbulent flow to any other. We show that δ(t) provides a useful quantitative characterization of any turbulent flow through generally only two parameters, its time average δ¯ and its variance δ2. These two quantities present topological and thermodynamical properties since they are connected, respectively, to the distance between the instantaneous and the time-averaged flow and to the number of degrees of freedom of the flow. Properties of δ¯ and δ2 are experimentally studied in the typical case of the von Karman flow and used to characterize the scale by scale energy budget as a function of the forcing mode as well as the transition be...

Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium

We report the first experimental observation of a bistable dynamo regime. A turbulent flow of liquid sodium is generated between two disks in the von Karman geometry (VKS experiment). When one disk is kept at rest, bistability is observed between a stationary and an oscillatory magnetic field. The stationary and oscillatory branches occur in the vicinity of a codimension-two bifurcation that results from the coupling between two modes of magnetic field. We present an experimental study of the two regimes and study in detail the region of bistability that we understand in terms of dynamical system theory. Despite the very turbulent nature of the flow, the bifurcations of the magnetic field are correctly described by a low-dimensional model. In addition, the different regimes are robust; i.e. turbulent fluctuations do not drive any transition between the oscillatory and stationary states in the region of bistability.

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 Kármán 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.

Large-scale flows in transitional plane Couette flow: A key ingredient of the spot growth mechanism

Using particle image velocimetry in a new experimental plane Couette flow, we investigate the dynamics of turbulent patches invading formerly laminar flows. We evidence experimentally for the first time in this geometry the existence of large scale flows. These flows appear as soon as laminar and turbulent domains coexist. Spectral analysis is used to study the dynamical evolution of these large scales as well as that of the small scales associated with turbulence. We show that large-scale flows grow before turbulent spots develop and we point out the crucial role they play in the growth mechanism and possibly also in the emergence of organised patterns.

Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined

A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum, and microscopic energy. Statistical equilibrium states are obtained by maximizing the Boltzmann entropy under these sole constraints. We assume that these constraints are selected by the properties of forcing and dissipation. The fluctuations are found to be Gaussian, while the mean flow is in a Beltrami state. Furthermore, we show that the maximization of entropy at fixed helicity, angular momentum, and microscopic energy is equivalent to the minimization of macroscopic energy at fixed helicity and angular momentum. This provides a justification of this selective decay principle from statistical mechanics. These theoretical predictions are in good agreement with experiments of a von Kármán turbulent flow and provide a way to measure the temperature of turbulence and check fluctuation-dissipation relations. Relaxation equations are derived that could provide an effective description of the dynamics toward the Beltrami state and the progressive emergence of a Gaussian distribution. They can also provide a numerical algorithm to determine maximum entropy states or minimum energy states.