Flood waves, which are resistance dominated, constitute the final category in the progression of wave types considered so far, ranging from the rapidly varying translatory waves, for which resistance could be neglected, to the intermediate category of tidal waves with their mixed character to the present case of flood waves, in which resistance is dominant.

Introduction

Flood waves are in essence humps of water traveling downriver. Stated in more detail, they are transient increases and decreases of discharge and water level (‘stage’) in a river caused by temporarily enlarged run-off in the catchment area due to heavy rainfall or snow melt, which travel downriver as a wave.

The temporal evolution and dynamics of flood waves differ greatly between the upper and lower reaches of a river. In the upper reaches, characterized by relatively steep slopes and a small catchment area, the response to an increased run-off can be quite fast, with rapid variations in flow rate and water level, even to the extent that inhabitants along the river border are taken by surprise, sometimes with fatal consequences.

In contrast, flood waves in the lower river reaches are slow processes, in many cases taking place over several days, due to the larger catchment area, the existence of tributaries and the greater propagation distance from upstream. Run-off peaks in different parts of the larger catchment area do not in general occur simultaneously, so that the maximum of their sum is less than the sum of the individual maxima. Moreover, as we will see, the internal dynamics of the flood wave cause it to flatten and to elongate as it propagates. As a result, the variations in flow rate and water level in the lower reaches are gradual, even such that inertia is insignificant (see Table 2.1 and Box 8.1).

In engineering practice, numerical models are used to simulate flood waves. These are based on the complete equations of De Saint-Venant (the long-wave equations), including inertia (see Chapter 11). This is needed in order to cover a wide range of occurrences of flood waves. Moreover, they should be able to cover the estuarine reaches of rivers, where tides penetrate, for which inertia and resistance are of comparable magnitude.