Stochastic dynamics of particles trapped in turbulent flows

The long-time dynamics of large particles trapped in two nonhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one-dimensional stochastic model of an overdamped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially nonhomogeneous fluctuations and a suited confinement strength

Open questions about homogeneous fluid dynamos: the VKS experiments

We consider several problems that arise in the context of homogeneous fluid dynamos such as the e ect of turbulence on the dynamo threshold, the saturation level of the generated magnetic eld above the threshold and its dynamics. We compare some of our predictions with the recent experimental results of the Karlsruhe and Riga experiments. Finally, we present the VKS experiment that we have designed to answer some of the remaining open questions. We study, in particular, the response of a turbulent flow to an external magnetic eld

Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow

We report an experimental study of the magnetic field ~BB induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic field ~BB0. We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, Rm. At low Rm, the induced mean field along the axis of the flow, hBxi, and the one parallel to ~BB0, hByi, first behave like R2 m, whereas the third component, hBzi, is linear in Rm. The sign of hBxi is determined by the flow helicity. At higher Rm, ~BB strongly depends on the local geometry of the mean flow: hBxi decreases to zero in the core of the swirling flow but remains finite outside. We compare the experimental results with the computed magnetic induction due to the mean flow alone

MHD measurements in the von Kármán sodium experiment

We study the magnetic induction in a confined swirling flow of liquid sodium, at integral magnetic Reynolds numbers up to 50. More precisely, we measure in situ the magnetic field induced by the flow motion in the presence of a weak external field. Because of the very small value of the magnetic Prandtl number of all liquid metals, flows with even modest Rm are strongly turbulent. Large mean induction effects are observed over a fluctuating background. As expected from the von Kármán flow geometry, the induction is strongly anisotropic. The main contributions are the generation of an azimuthal induced field when the applied field is in the axial direction ~an V effect! and the generation of axial induced field when the applied field is the transverse direction ~as in a large scale a effect!. Strong fluctuations of the induced field, due to the flow nonstationarity, occur over time scales slower than the flow forcing frequency. In the spectral domain, they display a f21 spectral slope. At smaller scales ~and larger frequencies! the turbulent fluctuations are in agreement with a Kolmogorov modeling of passive vector dynamics

Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow

We report an experimental study of the magnetic field ~BB induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic field ~BB0. We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, Rm. At low Rm, the induced mean field along the axis of the flow, hBxi, and the one parallel to ~BB0, hByi, first behave like R2 m, whereas the third component, hBzi, is linear in Rm. The sign of hBxi is determined by the flow helicity. At higher Rm, ~BB strongly depends on the local geometry of the mean flow: hBxi decreases to zero in the core of the swirling flow but remains finite outside. We compare the experimental results with the computed magnetic induction due to the mean flow alone

Stochastic dynamics of particles trapped in turbulent flows

The long-time dynamics of large particles trapped in two nonhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one-dimensional stochastic model of an overdamped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially nonhomogeneous fluctuations and a suited confinement strength