Motion of buoyant, flexible aquatic vegetation under waves: Simple theoretical models and parameterization of wave dissipation

Abstract

When submerged, flexible vegetation bends back and forth under waves, and stems are tilted only a small angle from vertical, simple models for stem motion and wave dissipation can be derived. Here, previous simple models for the wave-induced bending of elastic vegetation are extended to account for buoyancy. Buoyancy results in stem tension which, together with fluid drag, is incorporated in the Euler-Bernoulli problem, in which each stem is modeled as a cantilevered elastic beam. Solutions are governed by a new ‘dimensionless buoyancy’ β, in addition to the ‘dimensionless stiffness’ S identified by previous researchers. If β≪S1/2, buoyancy is negligible and previous results for elastic stems are recovered. Specifically, stems are nearly immobile for S≫1, but for S≪1 stems move with surrounding water except in a thin ‘elastic boundary layer’ extending a distance S1/4l* above the bed, where l*= stem length. Conversely, if β≫S1/2, then elasticity is negligible along most of the length of the stem and new behaviour is found. Specifically, stems are nearly immobile for β≫1, but for β≪1 stems move with surrounding water except in a thin ‘buoyant boundary layer’ extending a distance β1/2l* above the bed. For essentially inflexible cases (S≫1 or β≫1), simulated depth-integrated wave dissipation roughly equals the value Dr predicted for rigid stems. For highly flexible cases (i.e. for S and β both ≪1), dissipation is limited to elastic or buoyant boundary layers, and therefore scales with the maximum of S1/4Dr and β1/2Dr. For the simple stems considered here, which have constant diameter and density, simulated dissipation for all S and β was approximated by the expression [(S+β2/4)/(4+S+β2/4)]1/4Dr. This simple formula may require modification for vegetation with complex geometry. Nevertheless, this analysis identifies β as a key parameter for inclusion in dissipation formulations, together with parameters such as S identified by previous authors.