Unsteady Salinity Intrusion In Estuaries

The salinity structure of a tidal estuary fed by upstream fresh water sources is an important factor of water quality. In addition, this structure is intimately related to the circulation of the estuary because of density currents induced by the salt-fresh water relation. Previous investigations in two and three dimensions have been limited to extremely simplified geometrical and steady-state assumptions. One dimensional studies have considered the variable area case, but have been limited to descriptive rather than predictive methods because of the difficulty of handling the downstream boundary condition for the one-dimensional salt balance equation and because of the necessity to specify a longitudinal dispersion coefficient based on field data for the estuary being studied. This study presents a predictive numerical model of unsteady salinity intrusion in estuaries by formulating the problem in finite-difference terms using the one-dimensional, tidal time, variable area equations for the conservation of water mass, conservation of momentum and conservation of salt. Tidal time means a time scale of calculation larger than that defining turbulence, but much smaller than a tidal period in order to correctly represent the tidal advection within a tidal period. The tidal dynamic equations are coupled to the conservation of salt equation through a salinity-density relationship, and the ocean boundary condition for salt is formulated in a manner which depends on the direction of flow at the entrance to the estuary. The longitudinal dispersion coefficient has been shown to be proportional to the magnitude of the local, time-varying longitudinal salinity gradient, and this constant of proportionality has been shown to depend on a dimensionless parameter which expresses the degree of vertical stratification of the estuary. This relationship has been established for a wide range of stratification conditions. The mathematical model has been verified using data from the Waterways Experiment Station salinity flume and field data from the Delaware, the Potomac, and the Hudson. By specifying initial conditions, fresh water hydrographs, and tidal elevations at the ocean, it is possible to predict the time-varying salinity using this model.

Foreword: This report is intended as a documentation of the computer program and as a user's manual for the implementation of the mathematical model for the prediction of unsteady salinity intrusion in estuaries. The details of the model development and verification are contained in the following report: "A Mathematical Model for the Prediction of Unsteady Salinity Intrusion in Estuaries" by M. Llewellyn Thatcher and Donald R.F. Harleman, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 144, February 1972 also published by M.I.T. Sea Grant Project Office as Report No. MITSG 72-7 (index No. 72-307-Ccb)]. The unsteady salinity intrusion model is one-dimensional, although varying degrees of stratification are accounted for in the assumed longitudinal dispersion relationship. This model is a component in two additional studies, one of which is concerned with the two-dimensional aspects of salinity intrusion (i.e. vertical salinity and velocity distributions in estuaries): "Mathematical Simulation of Tidal Time-Averages of Salinity and Velocity Profiles in Estuaries" by John S. Fisher, John D. Ditmars and Arthur T. Ippen, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 151, July 1972 [also published by M.I.T. Sea Grant Project Office as Report No. MITSG 72-11 (index No. 72-311-Ccb)] The second study is concerned with the development of a model for predicting the transient longitudinal distribution of water quality parameters in estuaries: "Numerical Model for the Prediction of Transient Water Quality in Estuary Networks" by James E. Dailey and Donald R.F. Harleman, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 158, October 1972 [also published by M.I.T. Sea Grant Project Office as Report No. MITSG 72-15 (index No. 72-315-Ccb)] This user's manual therefore assists in the implementation of the analytical and numerical models listed above.

An experimental and analytical study of the basic factors which determine the instantaneous longitudinal distribution of salinity in a partially mixed estuary of constant section is presented. The mass-transfer equation is solved in two parts: (a) the quasi-steady-state convective-diffusion problem for an observer moving with the tidal velocity, and (b) the cyclic translation of saline water due to the tidal velocity. In the steady-state portion the apparent longitudinal diffusion coefficient is a function of the turbulence induced by the tide and of the internal circulations induced by the density difference. An expression is developed for the intrusion length as a function of the estuary length, mean depth, tidal amplitude and period, fresh-water discharge, ocean salinity, and estuary roughness. A stratification number is defined which expresses the degree of stratification or mixing in an estuary. (Author).

Multi-channel estuaries, such as the Mekong Delta in Vietnam and the Scheldt in the Netherlands, have characteristics of both the river and the sea, forming an environment influenced by tidal movements of the sea and freshwater flow of the river. This study discusses a predictive analytical approach for salinity intrusion and discharge estimate in multi-channel estuaries. The new approach agrees with 1-D hydrodynamic models and observations, indicating its applicability in practice. It has successfully developed a new theory and a new equation to quantify tidal pumping due to ebb-flood channel residual circulation and the related salt dispersion.