HARES
Introduction

In this example the wave penetration into the deep sea harbours of the Port of Rotterdam (The Maasvlakte) is presented. In the figures directly below an arial view of the Maasvlakte is given. Also the HARES model area is presented.

Arial view of the Maasvlakte HARES model area

The most relevant HARES model output is the so-called ‘wave height multiplication factor’ or K-factor. This K-factor is the ratio between the wave height in the model area (H) and the wave height at the boundary of the model area (H0). K = H/H0. At the boundary of the model K = 1.0. This K-ratio can be seen as the amplitude of the local wave climate.

The Maasvlakte and the entrance to the Port of Rotterdam (the Nieuwe Waterweg) is protected by the Northern breakwater (see above figures). The wave transmission through this Northern breakwater can not be neglected.

HARES can not directly account for wave transmission through breakwaters, so for a single wave direction the wave penetration is divided into two parts:

  • Normal calculation with an impermeable Northern breakwater
  • Transmission calculation in which the Northern breakwater acts as a wave boundary

    With a wave transmission coefficient R, the K factors of both calculations are combined to one, as follows:

    For a single harmonic wave with a wave period of 10 seconds and a wave direction of 325 degrees and example of how to account for wave transmission is given in the figure below. In this case a wave transmission coefficient R of 0.28 has been apllied, which corresponds with a water level of Mean High Water Spring (NAP +1.30m).

    Eaxmple of how to account for wave transmission

    One HARES simulation can deal with only one incoming wave direction. To include directional spreading, various HARES simulation runs are carried out with various incoming wave directions.

    The different HARES runs (n) can be combined to one as follows (linear wave theory):

    Results

    For this example the results of 4 wave periods and 8 main wave direction are presented.

    Situation 1:
    wave period: 6 seconds
    main wave direction: 280 to 350 degrees (nautical)
    directional spreading: 30 degrees at both sides of main wave direction

    Situation 2:
    wave period: 10 seconds
    main wave direction: 280 to 350 degrees (nautical)
    directional spreading: 15 degrees at both sides of main wave direction

    Situation 3:
    wave period: 15 seconds
    main wave direction: 280 to 350 degrees (nautical)
    directional spreading: 15 degrees at both sides of main wave direction

    Situation 4:
    wave period: 20 seconds
    main wave direction: 280 to 350 degrees (nautical)
    directional spreading: 15 degrees at both sides of main wave direction