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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The three-dimensional flow structure of a non-buoyant vertical round jet in a wave-current coexisting environment is investigated. Laboratory experiments are first conducted to measure instantaneous flow patterns and mean velocity fields of the jet in a wave-current coexisting environment and a current-only environment for comparison. The distinctive ‘effluent clouds’ phenomenon is clearly observed in the wave-current coexisting environment but scarcely observed in the current-only environment. Moreover, the mean velocity vectors bend further toward the bottom when the wave effect is present. To reveal a more detailed flow structure of the jet in the wave-current coexisting environment, a large eddy simulation (LES) model is developed and validated against the experimental data. The mechanisms of formation and development of ‘effluent clouds’ are unravelled based on in-depth analysis of the vorticity contours and the high-pass filtered flow fields on the vertical symmetrical plane. With the variation of instantaneous jet-to-current velocity ratio, the ‘effluent clouds’ dynamically interact with the current-induced counter-rotating vortex pair (CVP), resulting in an inverted pear-shaped distribution of mean flow field above the CVP structure centre. This study highlights that the existence of ‘effluent clouds’ can lead to a significant enhancement of jet spread and dilution in the wave-current coexisting environment. [ABSTRACT FROM AUTHOR]

• A general integral model is developed to simulate movement and dilution processes of jets in different dynamic environment. • Numerical results are found to be in good agreement with experimental data. • Each entrainment coefficient in the model can be taken as a constant. • The drag force coefficient varies with the jet-to-wave characteristic ratio. • The range of applicability of the model is carefully evaluated and several model limitations are proposed. An integral model for the simulation and prediction of the mixing and diffusion of submerged wastewater discharge in the form of a jet flow in a coastal dynamic environment is still lacking in the literature. In this study, a general integral model was developed to simulate and predict the movement and dilution process of jets in still water, currents, waves, and wavy current environments. Specifically, starting from the fundamental Navier–Stokes equations combined with the conservation equations of mass and scalar quantities, the equations of movement and the governing equations of mass, momentum, buoyancy, and scalar quantities were derived. Furthermore, the model employs an entrainment closure approach that distinguishes the contribution of transverse and azimuthal shear mechanisms and contains a quadratic-law turbulent drag force mechanism. A comparison with the basic experimental data for jets in still water, currents, waves, and wavy current environments supports the choice and magnitude of the entrainment coefficients contained in the entrainment formulation as well as the unified calculation formula of the drag force coefficient contained in the drag force formulation. The range of applicability of the model is carefully evaluated, and several model limitations, beyond which the integral model becomes invalid, are proposed. The general integral model provides a reliable technical approach to studying the movement and dilution process of jets in a wavy current environment and may be used to study the effects of waves and tidal currents on jets for a much wider range of source and ambient conditions than have been studied experimentally thus far. [ABSTRACT FROM AUTHOR]