Initial dilution of a vertical round non-buoyant jet in wavy cross-flow environment

The phenomenon of wastewater discharged into coastal waters can be simplified as a turbulent jet under the effect of waves and currents. Previous studies have been carried out to investigate the jet behaviors under the current only or the wave only environment. To obtain better understanding of the jet behaviors in a realistic situation, a series of physical experiments on the initial dilution of a vertical round jet in the wavy cross-flow environment are conducted. The diluted processes of the jet are recorded by a high-resolution camcorder and the concentration fields of the jet are measured with a peristaltic suction pumping system. When the jet is discharged into the wavy cross-flow environment, a distinctive phenomenon, namely “effluent clouds”, is observed. According to the quantitative measurements, the jet width in the wavy cross-flow environment increases more significantly than that does in the cross-flow only environment, indicating that the waves impose a positive effect on the enhancement of jet initial dilution. In order to generalize the experimental findings, a comprehensive velocity scale u_a and a characteristic length scale l are introduced. Through dimensional analysis, it is found that the dimensionless centerline concentration trajectories y_c/l is in proportion to 1/3 power of the dimensionless downstream distance x/l, and the dimensionless centerline dilution S_cQ/(u_al²) is proportional to the square of the dimensionless centerline trajectory y_c/l. Several empirical equations are then derived by using the Froude number of cross-flow Fr_c as a reference coefficient. This paper provides a better understanding and new estimations of the jet initial dilution under the combined effect of waves and cross-flow current.