Using Depth-Normalized Coordinates to Examine Mass Transport Residual Circulation in Estuaries with Large Tidal Amplitude Relative to the Mean Depth

Residual (subtidal) circulation profiles in estuaries with a large tidal amplitude-to-depth ratio often are quite complex and do not resemble the traditional estuarine gravitational circulation profile. This paper describes how a depth-normalized sigma-coordinate system allows for a more physical interpretation of residual circulation profiles than does a fixed vertical coordinate system in an estuary with a tidal amplitude comparable to the mean depth. Depth-normalized coordinates permit the approximation of Lagrangian residuals, performance of empirical orthogonal function (EOF) analysis, estimation of terms in the along-stream momentum equations throughout depth, and computation of a tidally averaged momentum balance. The residual mass transport velocity has an enhanced two-layer exchange flow relative to an Eulerian mean because of the Stokes wave transport velocity directed upstream at all depths. While the observed sigma-coordinate profiles resemble gravitational circulation, and pressure and friction are the dominant terms in the tidally varying and tidally averaged momentum equations, the two-layer shear velocity from an EOF analysis does not correlate with the along-stream density gradient. To directly compare to theoretical profiles, an extension of a pressure-friction balance in sigma coordinates is solved. While the barotropic riverine residual matches theory, the mean longitudinal density gradient and mean vertical mixing cannot explain the magnitude of the observed two-layer shear residual. In addition, residual shear circulation in this system is strongly driven by asymmetries during the tidal cycle, particularly straining and advection of the salinity field, creating intratidal variation in stratification, vertical mixing, and shear.