Ocean Dynamics

, Volume 61, Issue 11, pp 1719–1741 | Cite as

Analytical and numerical analysis of tides and salinities in estuaries; part I: tidal wave propagation in convergent estuaries

  • Leo C. van RijnEmail author


Analytical solutions of the momentum and energy equations for tidal flow are studied. Analytical solutions are well known for prismatic channels but are less well known for converging channels. As most estuaries have a planform with converging channels, the attention in this paper is fully focused on converging tidal channels. It will be shown that the tidal range along converging channels can be described by relatively simple expressions solving the energy and momentum equations (new approaches). The semi-analytical solution of the energy equation includes quadratic (nonlinear) bottom friction. The analytical solution of the continuity and momentum equations is only possible for linearized bottom friction. The linearized analytical solution is presented for sinusoidal tidal waves with and without reflection in strongly convergent (funnel type) channels. Using these approaches, simple and powerful tools (spreadsheet models) for tidal analysis of amplified and damped tidal wave propagation in converging estuaries have been developed. The analytical solutions are compared with the results of numerical solutions and with measured data of the Western Scheldt Estuary in the Netherlands, the Hooghly Estuary in India and the Delaware Estuary in the USA. The analytical solutions show surprisingly good agreement with measured tidal ranges in these large-scale tidal systems. Convergence is found to be dominant in long and deep-converging channels resulting in an amplified tidal range, whereas bottom friction is generally dominant in shallow converging channels resulting in a damped tidal range. Reflection in closed-end channels is important in the most landward 1/3 length of the total channel length. In strongly convergent channels with a single forward propagating tidal wave, there is a phase lead of the horizontal and vertical tide close to 90o, mimicking a standing wave system (apparent standing wave).


Tidal propagation Salinity Convergent estuary Prismatic channel Analytical model Numerical model 



J. Dronkers of Deltares is gratefully acknowledged for his suggestions and checks improving the manuscript. Also, PK Tonnon of Deltares/Delft Hydraulics is gratefully acknowledged for performing and analyzing the DELFT2DH model runs.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Deltares and University of UtrechtUtrechtThe Netherlands

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