It is often advantageous to model a semi-enclosed estuarine or coastal embayment (e.g. fish farms or tidal inlets, or typhoon shelters) as a separate system within a larger water body connected to the outer sea. The water quality of the system depends crucially on its flushing time-the average time of a particle in the system. The flushing time is governed by the barotropic and baroclinic tidal exchanges between the system and the outer sea. We describe herein a general method to determine systematically the flushing time of a stratified water body via a numerical tracer experiment. Numerical solution of the 3D flow and mass transport equations for many practical problems show that the tracer mass removal process depends on the physical topography and bathymetry, tidal range and the degree of stratification in the outer sea. Field application suggests that the tracer mass variation can be well approximated by a double-exponential decay curve that can be described by three flushing coefficients. Using a simple analytical two-segment model, the flushing coefficients can be given a clear physical interpretation, and the flushing time can be easily determined in terms of the coefficients. The method is illustrated by application to a number of tidal inlets in Hong Kong, in both the dry and wet season. The connection between the numerically determined flushing time and the traditional bulk flushing time obtained from salt balance methods is established.
In densely populated coastal cities in Asia, wastewater outfalls are often located not far from sensitive areas such as beaches or shellfisheries. The impact and risk assessment of effluent discharges poses particular technical challenges, as pollutant concentration needs to be accurately predicted both in the near field and intermediate field. The active mixing close to the discharge can be modeled by proven plume models, while the fate and transport far beyond the mixing zone can be well-predicted by three-dimensional ͑3D͒ circulation models based on the hydrostatic pressure approximation. These models are usually applied separately with essentially one-way coupling; the action of the plume mixing on the external flow is neglected. Important phenomena such as surface buoyant spread or source-induced changes in ambient stratification cannot be satisfactorily addressed by such an approach. A Distributed Entrainment Sink Approach is proposed to model effluent mixing and transport in the intermediate field by dynamic coupling of a 3D far field shallow water circulation model with a Lagrangian near-field plume model. The action of the plume on the surrounding flow is modeled by a distribution of sinks along the plume trajectory and an equivalent diluted source flow at the predicted terminal height of rise. In this way, a two-way dynamic link can be established at grid cell level between the near and far-field models. The method is demonstrated for a number of complex flows including the interaction of a confined rising plume with ambient stratification, and the mixing of a line plume in cross flow. Numerical predictions are in excellent agreement with basic laboratory data. The general method can be readily incorporated in existing circulation models to yield accurate predictions of mixing and transport in the intermediate/far field.
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