Revisiting linearized one-dimensional tidal propagation

In this paper we extend the validity of the classical linear solution for tidal hydrodynamics including the effects of width and depth convergence. Reworking such a solution in the light of externally defined, dimensionless parameters we are able to provide simple relationships to predict the most relevant features of the tidal wave at the estuary mouth (velocity amplitude, phase lag, wavelength, and damping) and to reproduce the main dynamics of tidal wave propagation along finite and infinite length channels. We also highlight the need for an accurate treatment of the linearized bed shear stress by exploiting an iterative procedure, and we show the improvement that can be reached by subdividing the entire estuary in shorter reaches. Different versions of the analytical solution are compared with numerical results, highlighting the strengths and weaknesses of the linear model.