New formulas for estimating initial dilution of buoyancy-dominated jets in a current

For buoyancy-dominated effluents discharged into moving water, three distinct regions are recognized: the buoyancy-dominated near field (BDNF), the buoyancy-dominated far field (BDFF), and an intermediate transition region. Most existing initial dilution formulas—derived from empirical and field studies—focus on the BDNF and BDFF regions while neglecting the transition zone. In this study, two new semi-empirical equations were developed using field and experimental data: one for submerged discharges and another for minimum surface dilution. These equations were calibrated via nonlinear regression, offering a unified approach to effectively calculating initial dilution across both the BDNF and BDFF regions while also addressing the transition region’s dilution in a single step. The proposed formulas were further validated through comparison with an earlier semi-empirical model using the same dataset.