This chapter deals with the modelling of translatory waves. The archetype of a translatory wave is a transient disturbance of discharge and surface elevation, travelling between two regions of uniform flow (including the state of rest as a special case). We will discuss the generation and propagation of these waves, considering uniform as well as non-uniform canals. The effect of bed resistance on translatory waves is marginal initially, but it can become important over long travelling distances. For this reason we will quantify the associated damping mechanism. A special type of translatory wave is the tidal bore, whose spectacular appearance alone, besides its intricate physics, would already motivate its treatment here.

Introduction

Translatory waves are usually the result of operation of engineering structures, such as

1. • locks

2. • control structures

3. • pumping stations

4. • hydropower plants.

Manipulation of these structures gives rise to varying discharges onto the adjacent canal reaches. For example, the levelling of the water in a lock chamber is accompanied by a discharge into or from the adjacent canal reach, which gradually increases from zero to maximum and then back to zero. This results in a transient disturbance in the canal in which the variation of the surface elevation mirrors that of the discharge, going from zero to an extreme (either a maximum or a minimum) and back to zero. The other three cases usually involve a gradual shift to a new setting, which is then left unchanged for quite some time; in such cases, the variation in discharge and surface elevation is monotonic (instead of going through a maximum or a minimum), and the resulting translatory wave forms a monotonic, moving transition between two different states of uniform flow.

The propagation of low translatory waves, and the relation between the changes in discharge and surface elevation, have already been considered in the preceding chapter. Here, we return to the subject by presenting some extensions dealing with propagation in nonprismatic channels and with the process of gradual damping due to boundary resistance, which is relevant in the case of long travel times and long propagation distances. All of this is based on the assumption of low waves, allowing linearization.