Numerical determination of flushing time for stratified water bodies

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.