Analytical and numerical analysis of tides and salinities in estuaries; part I: tidal wave propagation in convergent estuaries |
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| Authors: | Leo C van Rijn |
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| Institution: | (1) Deltares and University of Utrecht, Utrecht, The Netherlands |
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| Abstract: | 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). |
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