An advection-diffusion model for the dispersion in quasi two-dimensional steady turbulent jets

The study of turbulent jets in relatively enclosed geometries is relevant to many chemical engineering processes. Predicting the concentration of chemical reactants in time and space requires a good understanding of the jet dynamics. We have considered experimentally and theoretically the behaviour of liquid jets in a quasi-Hele-Shaw cell, where the jets are constrained in a narrow gap whose width is two orders of magnitude smaller than the length-scales of the other two flow dimensions. In this configuration, the dynamics shown by the jets is very rich. Detailed examinations of instantaneous structures of the flow reveal a high-speed sinuous core at the centre of the jet and large vortical structures on each side, which we analyse quantitatively using a variety of techniques (particle image velocimetry and dye experiments). These structures have a large impact on the mixing and dispersion properties of the jet. We propose a one-dimensional advection-diffusion model to account for the vertical dispersion in the jet. The diffusion coefficient assumed in the model is based on our understanding of the large-scale structures of these jets. The model is solved analytically using a similarity form in the case of a finite-volume release of tracers in the jet. The theoretical predictions and the experimental measurements show very good agreement.