OVERVIEW

As with all open channel flow, tidal flow in estuaries can be described by the St. Venant equations: a set of two non-linear partial differential equations that govern the movement of water through a medium. What makes tidal flow in alluvial estuaries different from other hydraulic phenomena is the medium through which the water flows. As we saw in the previous chapter, in coastal plains this medium has a particular shape, similar to the shape of an ideal estuary. Although this knowledge is far from new, in practice only few people make use of it, probably because modern computational power allows us to make three-dimensional computations that no longer require geometric simplification. The mere application, however, of computer models without the knowledge and insight provided by the use of analytical equations, is often dangerous. Analytical solutions not only provide insight into the processes at play, more importantly, they provide a means for verification or falsification.

This chapter describes the hydraulic equations of alluvial estuaries where there is a close interaction between geometry and flow, mutually influencing each other in continuous feedback. As a result, a regular topography appears in which mathematical laws can be discerned that can be described by surprisingly simple analytical equations. In combining the conservation of mass and momentum equations with the topography of an alluvial estuary, a number of analytical equations are derived for: 1) tidal propagation, 2) tidal damping, 3) tidal amplification, 4) wave celerity, 5) phase lag, and 6) the influence of river...