Importance of cross-channel bathymetry and eddy viscosity parameterisation in modelling estuarine flow

For a proper understanding of flow patterns in curved tidal channels, quantification of contributions from individual physical mechanisms is essential. We study quantitatively how such contributions are affected by cross-channel bathymetry and three alternative eddy viscosity parameterisations. Two models are presented for this purpose, both describing flow in curved but otherwise prismatic channels with an (almost) arbitrary transverse bathymetry. One is a numerical model based on the full three-dimensional shallow water equations. Special feature of this diagnostic model is that assumptions regarding the relative importance of particular physical mechanisms can be incorporated in the computations by switching corresponding terms in the model equations on or off. We also present an idealized model that provides semi-analytical approximate solutions of the shallow water equations for all three considered alternative eddy viscosity parameterisations. It forms an aid in explaining and theorising about results obtained with the numerical model. Observations regarding Chesapeake Bay serve as a reference case for the present study. We find that the relative importance of both along-channel advective forcing and transverse diffusive forcing depends on local characteristics of the cross-sectional bottom profile rather than global ones. In our reference case, tide-residual along-channel flow induced by these forcings is not small compared to the total tidal residual. Building on this observation, we present an indicative test to judge whether advective processes should be included in leading order in modelling tide-dominated estuarine flow. Furthermore, depending on the applied eddy viscosity parameterisation (uniformly or parabolically distributed over the vertical), we find qualitatively different spatial patterns for the along-channel advective forcing.