TABLE OF CONTENTS The flow of water in shallow layers such as occur in coastal estuaries, oceans, rivers, etc., is of obvious practical importance. The prediction of tidal current sand elevation sisvital for navigation and for the determination of pollutant dispersal which, unfortunately, is still frequently deposited there. The transport of sediments associated with such flows is yet another field of interest.
If the free surface flow is confined to relatively thin layers the horizontal velocities are of primary importance and the problem can be reasonably approximated in two dimensions. Here we find that the resulting equations, which include in addition to the horizontal velocities the free surface elevation, can once again be written in the same conservation form as the Euler equations studied in previous chapters [viz. Eq. (7.1)].
Indeed, the detailed form of these equations bears a striking similarity to those of compressible gas flow despite the fact that now a purely incompressible fluid (water) is considered. It follows therefore that:
The methods developed in the previous chapters are in general applicable.
The type of phenomena (e.g. shocks, etc.) which we have encountered in compressible gas flows can occur again.
It will of course be found that practical interest focuses on different aspects. The objective of this chapter is therefore to introduce the basis of the derivation of the equation and to illustrate the numerical approximation techniques by a series of examples.
The approximations made in the formulation of the flow in shallow water bodies are similar in essence to...
