The integral model developed by Chin (1988) for modelling a non-buoyant turbulent jet in wave environment is improved by introducing two new parameters, i.e., the jet spreading rate c₁ and the shortening rate p_e. The parameter c₁ is used to simplify the model by explicitly describing the radial velocity and scalar profiles under the assumption of “instantaneous” Gaussian distribution. By doing so, the governing equations can be easily solved by simultaneously integrating the conservation laws of momentum and scalars across the jet cross-section. The parameter p_e is used to shorten the initial length of zone of flow establishment (ZFE), so as to more accurately account for the wave effect on the jet initial dilution near the jet nozzle. The parameters are calibrated by the particle image velocimetry (PIV)-measured data from three groups of jet experiments, i.e., the group of vertical jet towards the wave direction (vertical jet), the group of horizontal jet along the wave direction (co-wave jet) and the group of horizontal jet opposing to the wave direction (op-wave jet). The results show that both parameters are well related to the ratio of jet and wave characteristic velocities in the same group, but it is not able to be generalized among different groups. Under the same wave condition, the value of c₁ in the vertical jet is larger than that of the horizontal jets; while the value of p_e in the vertical jet is smaller than that of the horizontal jets, which indicates that the jet has a faster decay rate of centerline velocity and a wider width of jet cross-section profile in the near field when it is vertically discharged into the wave environment. With the well-calibrated parameters, the improved model can achieve a higher accuracy than the original model developed by Chin (1988).

The multiport diffuser effluent discharge facilities constructed beneath the coastal waters were simplified in the laboratory as twin buoyant jets in a wavy cross-flow environment. The near-field flow structure of twin jets was studied by series of experiments conducted in a physical wave–current flume. The particle image velocimetry (PIV) system was used to measure the velocity field of the jets in various cross-flow-only and wavy cross-flow environments. By means of flow visualization, the distinctive “effluent cloud” (EC) phenomenon was clearly observed and the jet penetration height was found to be notably increased compared with that of cross-flow-only environment at the downstream position. It was found that the wave-to-current velocity ratio R_wc is a very important parameter for effluent discharge. A new characteristic velocity u_ch and the corresponding characteristic length scale l_mb for twin buoyant jets in the wavy cross-flow environment were defined. Using curve-fitting, a new equation to estimate the effects of the jet-to-current velocity ratio (R_jc), wave-to-current velocity ratio (R_wc) and Strouhal number (St) on the jet trajectory were derived to enhance understanding the physical processes underpinning the rise and the dilution of buoyant jets, which is critical to the design of discharge facilities.

The pervasive discharge of high-density microplastics (HDMPs) from wastewater treatment plants (WWTPs) into aquatic ecosystems represents a critical environmental and engineering challenge. While conventional WWTPs achieve moderate removal efficiencies (60%–99%), their performance is highly variable for larger, denser particles (e.g., polyvinyl chloride, polyethylene terephthalate) due to complex interactions between particle characteristics (e.g., size distribution, shape anisotropy, and biofilm colonization), fluid dynamics (e.g., turbulent kinetic energy, and shear stresses), and process design parameters (e.g., retention times, and tank geometries). This review systematically evaluates the fate and transport dynamics of HDMPs in WWTPs, highlighting the underexplored role of dimensionless parameters (e.g., Shields parameter θ, particle Reynolds number Re _p , Stokes number St, Densimetric Froude number Fr′, particle shape factors ψ, Rouse number Z, and biofilm buoyancy number B _f ) in predicting their behavior across treatment stages and post-discharge environments. The study critically assesses knowledge gaps in existing removal technologies, ranging from membrane bioreactors (fouling risks) to emerging techniques such as electrocoagulation (energy costs), and identifies methodological shortcomings in sampling, analysis, and reporting that hinder global comparability. Key findings reveal that particle–fluid interactions (e.g., resuspension thresholds, and turbulent mixing) are poorly quantified for HDMPs, necessitating the development of revised hydrodynamic models that incorporate shape factors and biofilm effects. Additionally, synergistic stressors (e.g., temperature, and co-pollutants) are found to exacerbate ecological risks but remain understudied. Meanwhile, standardised protocols for HDMP characterisation and dimensionless parameter frameworks are urgently needed to unify research and policy efforts. The study proposes three priority research directions: (i) development of cost-effective, scalable hybrid systems (e.g., coagulation-membrane bioreactors); (ii) integration of dimensionless parameters into WWTP design and outfall modelling; and (iii) long-term studies on HDMPs’ ecological impacts under realistic exposure scenarios. By bridging fundamental hydrodynamics with applied engineering, this review provides a roadmap to mitigate HDMP pollution through science-informed policy and innovation.