Turbulent viscosity and turbulent magnetic diffusivity in a decaying spin-down flow of liquid sodium

Abstract

The free decay of a strong flow of liquid sodium (at Reynolds number defined via the maximal mean velocity and the radius of the channel cross section up to Re≈3×10(60) and the corresponding magnetic Reynolds number up to Rm≈30) generated by the sudden stop of a rapidly rotating toroidal channel is studied experimentally. The toroidal and poloidal components of velocity are measured using a potential probe. We describe the onset of motion, the evolution of strongly anisotropic fluctuations, and the homogenization and decay of turbulence in the final period. We analyze the statistical characteristics of velocity fields in relation to the behavior of effective magnetic diffusivity estimated from measurements of the phase shift between the induced and applied magnetic fields. For the late (self-similar) decay of turbulent flow, turbulent viscosity is shown to be dependent on the root-mean-square velocity pulsations and can be expressed as νt∼νRe1.3. The behavior of turbulent magnetic diffusivity depends on the magnetic Reynolds number defined in terms of the root-mean-square velocity pulsations. At low magnetic Reynolds numbers (Rmrms<1), turbulent magnetic diffusivity grows rapidly with increasing velocity pulsations (ηt∼ηRmrms2). If the magnetic Reynolds number exceeds unity, the behavior of turbulent magnetic diffusivity becomes similar to the behavior of turbulent viscosity. The highest values of turbulent magnetic diffusivity are achieved at the end of braking, which corresponds to the transient stage of a strongly anisotropic turbulent flow in which the poloidal velocity oscillations prevail.