Mixing behavior equations created by a buoyant jet in wavy crossflow environments

The understanding of mixing behaviors of submerged effluent discharge in buoyant jet flows within coastal dynamic environments remains incomprehensive. This study explores the mixing behaviors of buoyant jets in wavy crossflow environments by utilizing dimensional analysis and an integral model. We examine physical mechanisms underlying the linear uplift of buoyant jets and establish three semi-empirical equations pertaining to the vertical location of the cross-sectional minimum dilution, cross-sectional minimum dilution, and visible diffusion area. These equations quantify the influence of waves and buoyancy on the mixing behaviors of buoyant effluent discharge in wavy crossflow environments. The dimensional analysis demonstrates that the proposed mixing behavior equations are closely related to the buoyant characteristic length scale. We validate the reliability of these equations with that of existing ones for non-buoyant jets in wavy crossflow environments. Furthermore, this study extends the application of buoyant jet equations, evaluating their suitability by comparing them with data from cases involving buoyant jets in wavy crossflow environments. This study highlights the positive effect of wave height and buoyancy on the initial dilution of effluent discharge. Future studies can implement our semi-empirical equations on the near and far zone coupling simulations of wastewater and thermal discharges.