The relation of turbulence to diffusion in open-channel flows

Abstract

This investigation examines the interrelation between turbulent diffusion, dispersion, and the statistical properties of turbulence in an open-channel flow. The experiments were conducted in a 3. 87- foot wide flume over four boundary roughnesses. The results are from studies made of: (1) the influence of turbulence on the vertical and lateral diffusion of plumes of heated water and a neutrally-buoyant salt solution from a point source at the mid-depth of flow; (2) the velocity concentration covariance along the axis of a salt solution plume using a single-electrode conductivity probe and hot-film sensor; (3) lateral and longitudinal surface diffusion measured by dropping polyethylene particles on the water surface; and (4) longitudinal space-time velocity correlation measurements. The results of the study substantiate Philip's concept relating the ratio of Eulerian to estimated Lagrangian time scales and the reciprocal of the longitudinal intensity of turbulence. The relation is used to predict coefficients of longitudinal turbulent diffusion at the water surface and in the flow field. A similar concept using an integral time scale based on the longitudinal intensity of turbulence is used to predict coefficients of both surface and depth-averaged turbulent diffusion in three coordinate directions for heated water and neutrally buoyant jets of salt solution. Longitudinal space-time velocity correlation measurements can be used to predict the Lagrangian time scale only under limited conditions. For this study the Lagrangian scale was underpredicted by 250 percent. A model is developed for the behavior of the longitudinal velocity concentration covariance along the axis of a plume of neutrally-buoyant salt solution. The covariance measurements are accurate to ±20 percent . The boussinesq model of scalar transport is verified with an accuracy of ±25 percent by comparing diffusion coefficients from (1) the velocity concentration covariance measurements with (2) those obtained at the water surface using floating particles. The hot-film single-electrode conductivity probe method for measuring the covariance offers a new tool to experimenters in turbulent mass transfer. Under the range of conditions studied, longitudinal diffusion accounts for 4 to 13 percent of the one-dimensional dispersion process. Predictions of the dispersion coefficient by formulas such as Elder's were in error by as much as 50 percent. The exponent in the power-law equation describing the decay of scalar quantities downstream of a jet is a linear function of the shear velocity of the channel. The length of the core region of a jet is a power-law function of the jet strength with the exponent depending on boundary roughness.