Hydraulics research, HARES Examples, Introduction directional spreading

Svašek Hydraulics

Coastal, harbour and river engineering consultants


HARES Examples

Introduction directional spreading

The directional spreading is characterised by the parameter S_max. Small values of S_max correspond with a large amount of directional spreading whereas large values of S_max indicate nearly unidirectional waves. Typical values are:

  • S_max = 10; wind waves with a lot of directional spreading
  • S_max = 25; swell with short to intermediate decay distances
  • S_max = 75; swell with long decay distances (nearly unidirectional waves)
  • The amount of directional spreading for various values of S_max can be found in Figure 1, showing the cumulative curves of relative wave energy.

Figure 1

One HARES simulation can deal with only one incoming wave direction. To include directional spreading, various HARES simulations will have to be carried out with various incoming wave directions. The various directions and their share to the total wave energy depend on the value of S_max.


In a narrow harbour basin (see Figure 2), with slopes and some vertical quays, the effects of a wind generated wave field is investigated. The wave period is 4 seconds and the main wind direction is taken in the orientation of the basin. Figure 3 shows the wave energy distribution used to studie this harbour basin. So a total of 9 HARES runs has been made.

Figure 3


The 9 individual HARES runs are presented below in a slideshow.
Each figure shows the wave height multiplication factor (click image)

These individual HARES runs can be composed to one as follows:

The result is shown below.

Composed HARES run
wave period = 4 seconds
main wave direction = 307 degrees (nautical)
directional spreading included