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Phase‐Averaged Drag Force of Nonlinear Waves Over Submerged and Through Emergent Vegetation
Author(s) -
Zhu Ling,
Chen Qin
Publication year - 2019
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
eISSN - 2169-9291
pISSN - 2169-9275
DOI - 10.1029/2018jc014867
Subject(s) - vegetation (pathology) , wave height , drag , nonlinear system , waves and shallow water , wavelength , airy wave theory , wind wave , wave shoaling , dissipation , geology , phase (matter) , breaking wave , mechanics , wave propagation , hydrology (agriculture) , physics , stokes wave , geotechnical engineering , mechanical wave , oceanography , longitudinal wave , optics , medicine , pathology , quantum mechanics , thermodynamics
Aquatic vegetation protects the shoreline by dissipating the wave energy and reducing the mean water level. For the latter, the phase‐averaged depth‐integrated drag force induced by vegetation (F d ‾ ) plays an essential role. For linear waves, theF d ‾ exerted by submerged vegetation (F d sub ‾ ) and by the submerged part of emergent vegetation (F d trough ‾ ) equal 0. As the wave nonlinearity increases, the profile of the horizontal velocity ( u ) becomes skewed and non–cosine shaped, and thus, bothF d sub ‾ andF d trough ‾ are nonzero (phase average of u | u |≠0) and their significance increases. This study examines the effects of wave nonlinearity and vegetation submergence onF d ‾ based on stream function wave theory. In deep water, it is found that the wave nonlinearity slightly affectsF d trough ‾ due to the negligible weight ofF d trough ‾ in the overallF d ‾ . Both the wave nonlinearity and vegetation submergence have negligible effects onF d sub ‾ as well. In shallow water,F d trough ‾ takes up a large percentage in the overallF d ‾ for emergent vegetation, and a linear relationship betweenF d sub ‾ and vegetation submergence exists for waves with relatively small wave heights. The applicable range of the linear wave theory basedF d ‾ is determined usingF d ‾ from stream function wave theory as a reference solution. Moreover, a parametric model is developed for evaluatingF d ‾ for random waves. The mean water level changes, or wave setup, on a vegetated sloping beach are validated and quantified using experimental data obtained from literature.