Mass transport in turbulent Couette-Taylor flow

We have studied mass transport in a turbulent flow with large coherent structures—turbulent Taylor vortices. A pulse of dye is injected in fluid contained between concentric cylinders (with the inner one rotating and the outer one fixed), and the time dependence of the dye concentration at two axial positions is then determined from optical absorption measurements. The measurements have been made for radius ratios η ranging from 0.494 to 0.875, and at Reynolds numbers R ranging from 50 to 1000 times that corresponding to the onset of Taylor vortex flow. Transport in the axial direction is found to be modeled very well by a one-dimensional diffusion process with the reflections at the ends of the annulus and the finite injection time of the dye taken into account. (The time scale for the transport in the radial and azimuthal directions is short compared with that in the axial direction.) The effective axial diffusion coefficient D in the parameter range studied is of the order of 1 ${\mathrm{cm}}^2$/s, or greater, orders of magnitude larger than molecular diffusion coefficients. For a fixed R and η, D increases linearly with the axial wavelength λ of the Taylor vortices. The Reynolds-number dependence of the wavelength-independent scaled diffusion coefficient $D^{\mathrm{*}}$=(2d/λ)D (where d is the gap between the cylinders), is described by a power law $D^{\mathrm{*}}$∝$R^{\beta }$. Measurements for different parameter regions yield 0.69<β<0.86, while theory suggests a larger value, β=1.