Estuarine salt conservation: a Lagrangian approach

Abstract

Understanding tidal and mean flow transport mechanisms that maintain the estuarine salt balance against seaward transport by river flow is one of the fundamental questions of estuarine oceanography. Previous salt transport studies have failed to resolve this problem for two principal methodological reasons, in addition to the inherent variability of estuaries. First, salt transport expansions used to represent the salt balance have included a large number of terms that could not be related to any theory of estuarine circulation and whose physical meaning was thus unclear. Second, it has proven difficult to measure small mean velocities in the presence of much larger tidal variations. A new analysis method that expresses Lagrangian scalar property transport in terms of time and space variations of Eulerian variables is much simpler than expansions previously used and yields new insights into estuarine transport processes. This approach (like previous expansions) is valid for narrow systems in which cross-channel transport processes are weak and the ratio of tidal amplitude to mean depth is small. A surface boundary condition is used to eliminate one class of troublesome terms. The equivalence of the tidal-cycle average transport of tidal variations in salinity and the Stokes transport of mean salinity is then employed to show that the vertically integrated tidal flow plays no role in the overall salt balance. That is, seaward transport of salt caused by the river flow can only be balanced by landward transport resulting from correlations between shear and stratification in the mean, tidal and overtide flows. In a hypothetical inviscid estuary, tide and overtide flows would be vertically uniform, and outward fluvial salt transport could only be balanced by shear and stratification in the mean gravitational circulation. In a more realistic example with strong friction, the gravitational circulation would be severely damped, and inward transport could only be accomplished by correlations of shear and stratification in the tide and overtide flows.