Long-term memory in experiments and numerical simulations of hydrodynamic and magnetohydrodynamic turbulence.

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von Kármán swirling flow between two counterrotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field and a case with self-sustained magnetic fields. Evidence of long-term memory and 1/f noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von Kármán flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large-scale magnetic field.

Fluid mixing in stratified gravity currents: the Prandtl mixing length.

Shear-induced vertical mixing in a stratified flow is a key ingredient of thermohaline circulation. We experimentally determine the vertical flux of momentum and density of a forced gravity current using high-resolution velocity and density measurements. A constant eddy-viscosity model provides a poor description of the physics of mixing, but a Prandtl mixing length model relating momentum and density fluxes to mean velocity and density gradients works well. For the average gradient Richardson number Ri(g) approximately 0.08 and a Taylor Reynolds number Re(lambda) approximately 100, the mixing lengths are fairly constant, about the same magnitude, comparable to the turbulent shear length.

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

We report an experimental study of the magnetic field B--> induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic field B-->(0). We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, R(m). At low R(m), the induced mean field along the axis of the flow, , and the one parallel to B-->(0), , first behave like R(2)(m), whereas the third component, , is linear in R(m). The sign of is determined by the flow helicity. At higher R(m), B--> strongly depends on the local geometry of the mean flow: 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.