General integral model for a jet in wavy current environment

Abstract

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.