residual circulation in macrotidal, shallow estuaries

the large tidal range relative to the mean depth is clear in this plot of the tidally varying along-stream velocity

I am interested in understanding the dynamics in macrotidal, shallow estuarine environments where the change in tidal elevation is similar to the total water depth. In these systems, traditional estuarine dynamics often break down as non-linear effects dominate. Residual circulations and fluxes in these systems do not resemble expected profiles and require a different approach to understanding their meaning.

We have found that a successful way to interpret residual circulations in macrotidal, shallow estuaries is to convert to a sigma coordinate system, i.e. coordinates that follow the water surface. In this coordinate system we have been able to define approximate Lagrangian residuals (mass transport velocity, or the residual path that particles would take) show that particles experience a stronger shear circulation than would be interpreted from the Eulerian residual alone. We also can perform an Empirical Orthogonal Function Analysis on the sigma coordinate data that breaks the results into a barotropic residual and a shear residual. Interestingly in z coordinates this resembles a shear residual in the traditional sense (inflow at depth, outflow near the surface) and a barotropic residual in the reverse sense due to the barotropic tidal wave propagation. In the Snohomish River Estuary, the shear residual is driven not only by the longitudinal density gradient but also to an even greater degree by intratidal variations in stratification and vertical mixing and by lateral processes.

For more information on the sigma coordinate analysis, please see this paper.