A frequency distributed dissipation model for canopies

Niels G. Jacobsen (Corresponding Author), Brian C. McFall, Dominic A. Van der A

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13 Citations (Scopus)
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Existing dissipation models (bulk and frequency distributed) describing the wave attenuation in canopies rely on a characteristic shape of the velocity profile and corresponding characteristic frequency, which is integrated analytically over the height of the canopy. This means that all frequencies higher than the characteristic peak frequency are assigned excessive dissipation, while all frequencies lower than the characteristic peak frequency are assigned insufficient dissipation.

The present work presents a new dissipation model, which is given in a closed form based on the surface elevation spectrum, Sn . The model calculates the frequency dependent dissipation at a given vertical elevation z, which is numerically integrated over the height of the canopy. A comparison with existing bulk dissipation models shows that there are large differences between the existing models and the present work. These differences are particularly noticeable for realistic peak enhancements factors for the JONSWAP spectrum (1.0–10.0) and submerged canopies.

A comparison with the frequency distributed dissipation model in the spectral wave model SWAN is also presented and the present model distinguishes itself by naturally incorporating a cut-off frequency above which the dissipation effectively vanishes. This offers a more realistic frequency distribution of the dissipation. The frequency distribution of the dissipation and the existence of a frequency cut-off is verified with experimental data.
Original languageEnglish
Pages (from-to)135-146
Number of pages12
JournalCoastal Engineering
Early online date27 Apr 2019
Publication statusPublished - Aug 2019

Bibliographical note

Robert C. Houseago (University of Hull) conducted the data collection with assistance from University of Aberdeen students Ross Horgan and Rory Summers. The artificial vegetation flexibilities and densities were designed by Robert C. Houseago as part of his University of Hull funded PhD study on the effect of flexibility on in-canopy hydrodynamics. The University of Aberdeen wave flume experiments were supported by the European Communitys Horizon 2020 Programme through the grant to the budget of the Integrated Infrastructure Initiative HYDRALAB+, Contract no. 654110. The support of Mary Anderson Bryant and Jane Smith for providing their insight is graciously acknowledged. The support of the Coastal Structures and Wave Department of Deltares is acknowledged. This work was funded by the U.S. Department of Defense and Deltares through the Engineer and Scientist Exchange Program (ESEP) and the U.S. Army Corps of Engineers through the Engineering With Nature® (EWN®) initiative.


  • vegetated canopies
  • spectral energy dissipation
  • Vegetated canopies
  • Spectral energy dissipation


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