Turbulence in Rotating Flows

François Daviaud, Olivier Dauchot and Bérengère Dubrulle

**Quasi-linear model of turbulence** We have developed a new quasi-linear model of turbulence in collaboration with J.-P. Laval (Lille University) and S. Nazarenko (Warwick, GB). We have shown that this model allows simple understanding of the small scale intermittency. With J. Mc Williams (UCLA), we have also shown how this model could lead to a stochastic approach of the closure problem of Navier-Stokes equations. This method has been applied to the computation of 2D and 3D energy spectra in fluid turbulence with O. Zagorosvski (Warwick, GB), and to the computation of torques in von Karman experiment. The quasi-linear model of turbulence has also been applied to convection. The scaling laws of the turbulent transport have been derived. Logarithmic corrections to scaling have been obtained. This approach has been generalized to the case of large Prandtl number convection, leading to an explanation for an experimental controversy between several experiments.

Mean velocity field; the left side (resp. right side) of the figure represents the azimutal (resp. poloidal) flow; the propellers are situated at the top and bottom.

**Von Karman flows** Von Karman water experiment. (a) Mean velocity field the left side (resp. right side) of the figure represents the azimutal (resp. poloidal) flow; the propellers are situated at the top and bottom. (b) bifurcation diagram representing the torques C_1 and C_2 of the two motors as a function of the arctangent of the ratio of the two frequencies (225 corresponds to f_1=f_2); circles correspond to the usual flow and squares and diamonds to the bifurcated flow. The generic term von Karman flows designates the class of flows induced by the counter-rotation of two coaxial impellers located at both ends of a cylindrical vessel. These flows display differential rotation and large scale helicity and are supposed to be good candidates to the realization of an experimental homogeneous fluid dynamo. We have studied such flows in a water experiment, half-scale model of the sodium VKS experiment presented in the following. Different propellers have been used to drive the flow at rotation rates corresponding to a highly turbulent flow (Re = 5.10^5 ) and we have characterized the flow both globally (visualization, torque) and locally (pressure and velocity). Measurements of the mean velocity field have been performed by laser velocimetry techniques and reveal the existence of two counter-rotating toroidal cells combined with two recirculating poloidal cells. Note that velocity fluctuations appear to be of the order of magnitude of the mean velocity, in particular in the equatorial plane, where a strong mixing layer is observed.

#285 - Last update : 11/04 2009

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