Initial dilution equations for wastewater discharge: Example of non-buoyant jet in wave-following-current environment

In this study, three semi-empirical equations are developed to quantify the wave effect on the initial dilution of wastewater discharge, which usually forms a turbulent jet. To develop the equations, data from a non-buoyant jet in a wave-following-current environment, which is realised using a three-dimensional large eddy simulation model, are used with 27 cases in total. The effects of the wave-to-current velocity ratio, jet-to-current velocity ratio, and Strouhal number are considered in the equations. The initial dilution equations, which focused on the jet visual area, cross-sectional minimum dilution, and vertical location of the cross-sectional minimum dilution, have vital relationships with the characteristic length scale. The reliability of the present equations is discussed by comparing them with existing equations for a jet in a crossflow-only environment. The applicability range of the present equations is illustrated by comparing them with data for a jet in a crossflow-only environment and data for other cases of a jet in a wave-following-current environment. The three equations provide references for the conceptual design of wastewater discharge. This study reveals that a surface wave with low energy has a positive effect on the initial dilution of wastewater discharge.