Significant developments in hydraulics illuminate processes that occur in estuaries, including equations for flow in fully stratified, partially and well-mixed estuaries. The analytical solutions, mostly one-dimensional to date, are very useful in predicting the effects of changes in the estuary regime on salinity intrusion and shoaling patterns.
Stratified estuaries have a discontinuous interface between salt water and fresh water across which very little mixing occurs. In channels, unbalanced downstream pressure forces near the fresh-water end overcome the frictional resistance at the interface and contribute to an increase of the velocity head; at the salt-water end an unbalanced pressure force drives salt water upstream near the bottom. Analytical expressions exist for interfacial stability, mixing, and interfacial and bed shear stresses. The hydraulic equations predict increase in the salt-water intrusion length with increase of channel depth or decrease of fresh-water flow. In real estuaries, tides generate shearing stresses that break the interface and mix salt water and fresh water.
When the salinity difference between top and bottom of an estuarial channel is less than 10 percent, the estuary is termed well mixed; otherwise it is classified as partially mixed. Mixing increases with increasing tidal amplitude, and decreasing fresh-water flow. Continuous entrainment, mixing, upstream and downstream salt-water movement induce a net upstream flow of salt water near the bottom, just as in the fully stratified case, when the average transport over a tidal period is considered. Mixing is a complex combination of turbulent eddy diffusion, longitudinal dispersion, and gravitational convection. Experimentally, the diffusion coefficient depends on the rate of dissipation of energy due to tidal forces and the degree of vertical mixing. Vertical mixing usually is downward in the first half of the intrusion length but upward in the second half and depends on the degree of stratification. The longitudinal salinity distribution also depends on stratification. Stratification in real estuaries is affected by the tidal prism, the tidal Froude number, fresh-water discharge, and tidal period. Hydraulic relations between these factors and stratification are valid in a wide range of experimental and natural channels. The basic salt-water intrusion parameters have to be correlated with flow variables and estuary characteristics for complex geometries. The bed shear stresses, which are particularly important in predicting the location and rate of shoaling of fine-grained sediment, need further definition in natural estuarine systems. The analytical and experimental hydraulic approach, however, has proved useful in solving many problems in estuaries.