The Propagation of Tides up Rivers With Special Considerations on the Upper Saint Lawrence River

The hydrodynamics of rivers affected by tides is dominated by the damping and the distortion induced by quadratic bottom friction. A compact and accurate approximation to the deceleration term, standing for the frictional effect, allows the retention of the concept of harmonics and separation of the time and space variations. It then becomes possible to explain, in terms of basic physics, the transformation of the tide from the estuary, to the zone where it becomes extinct. The theoretical reasoning is supported by pertinent observations collected in the Saint Lawrence river; numerical relations are derived to demonstrate the existence of non-linear effects and to quantitatively link various relevant physical parameters. This analysis, in turn, helps outline approaches to improve the tide predictions in such rivers which happen to have such great economic and strategic importance.