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 ua and a characteristic length scale l are introduced. Through dimensional analysis, it is found that the dimensionless centerline concentration trajectories cy/l is in proportion to 1/3 power of the dimensionless downstream distance x/l, and the dimensionless centerline dilution 2c aS Q/（u l） is proportional to the square of the dimensionless centerline trajectory cy/l. Several empirical equations are then derived by using the Froude number of cross-flow Frc 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.
A generic numerical model using the large eddy simulation （LES） technique is developed to simulate a non-buoyant vertical jet in wave and/or current environments. The experimental data obtained in five different cases, i.e., one case of the jet in a wave only environment, two cases of the jet in a cross-flow only environment and two cases of the jet in a wave and cross-flow coexisting environment, are used to validate the model. The grid sensitivity tests are conducted based on four different grid systems and the results illustrate that the non-uniform grid system C （205x99x126 nodes with the minimum size of 1/10 jet diameter） is sufficiently fine for the modelling. The comparative study shows that the wave-current non-linear interaction should be taken into account at the inflow boundary while modelling the jet in wave and cross-flow coexisting environments. All numerical results agree well with the experimental data, showing that： （1） the jet under the influence of the wave action has a faster centerline velocity decay and a higher turbulence level than that in the stagnant ambience, meanwhile the ＂twin peaks＂ phenomenon exists on the cross-sectional velocity profiles, （2） the jet under a cross-flow scenario is deflected along the cross-flow with the node in the downstream, （3） the jet in wave and cross-flow coexisting environments has a flow structure of＂effluent clouds＂, which enhances the mixing of the jet with surrounding waters.
