An Eddy-Based Model and Measurements of the Ekman-induced Turbulent Transport of Momentum and Magnetic Flux in the Liquid Sodium a?-Dynamo Experiment:

The two coherent motions, rotational shear, the ``$w$-effect,'' and pulsed unidirectional plume-driven helicity, the ``$a$-effect,'' of the Liquid Sodium $aw$-Dynamo Experiment at NMIMT depends upon the two orthogonal instability-constrained, low turbulent flows. The stability of the $w$-effect is achieved by stable Couette flow, $dw/dr >0$, (that of the ``$a$-effect by the transient nature of the plumes.) The effective ``$w$-gain'' of the Couette shear flow, (experimentally measured $\times 8$) is limited by both the magnetic diffusivity of liquid sodium, $h$~750 cm$^2/s$, $Rm \sim 120$, and the diffusivity of the turbulence induced by the Ekman flow. We measure the torque induced by the Ekman flow, thickness, $h\sim r Re^{-1/2}$, $Re\sim 10^7$ and infer the velocity distribution from pressure measurements vs radius. A comparison is then made with an eddy-based theory of turbulence, 1) a laminar sub-layer, 2) log-law of the walls eddy size distribution, and 3) an eddy size truncated at the scale of the Couette shear stability. With this eddy size and stress distribution a turbulent velocity distribution is compared to the measured pressure distribution, and the $w$-gain. Supported by the DOE.