The category of long waves encompasses different wave types, each with a different origin and with different dynamics, in the sense that the relative importance of the various physical processes, as expressed by the different terms in the equation of motion, can vary. In this chapter we will first give an overview of the various types of long wave and their generation, and we will verify formally that they can indeed be classified as ‘long’. Next, we will estimate the relative magnitudes of terms in the equation of motion, which provides an ordering of wave types based on the importance of inertia relative to the resistance.

Types of Long Waves

In general, one can say that the faster the flow varies, the more important will be the inertia relative to the resistance, and the more it will be in balance with the net driving force. Before dealing with these dynamics we give short descriptions of the origin and typical characteristics of the different types of long waves:

1. • translatory waves (transient variations in discharge and water level, usually caused by operation of controls)

2. • tsunamis (sea waves generated by subsea earthquakes, volcanic eruptions etc.)

3. • seiches (standing oscillations in lakes, bays, harbours etc.)

4. • tides in oceans, shelf seas, estuaries and lowland rivers

5. • flood waves in rivers

Translatory Waves

As a result of manipulation (or breakdown!) of pumps or valves in the operation of locks, weirs, evacuation sluices, hydropower plants, etc., variations in discharge (δQ) can occur. These are accompanied by variations in water surface elevation (δh). Such disturbances travel as so-called translatory waves into the adjacent reaches of the conduit. The passage of such wave induces a rise in elevation in the case of an increase in discharge, and a lowering in the case of a decrease in discharge; see Figure 2.1. The particle velocities in a translatory wave are in one direction only (either forward or backward), which explains the name ‘translatory waves’, as opposed to ‘oscillatory waves’, in which the particles move back and forth.