Wave-forced motion of submerged single-stem vegetation

Abstract

We derive an analytical model for the wave-forced movement of single-stem vegetation and test the model against observed vegetation motion in a natural salt marsh. Solutions for constant diameter and tapered stems are expanded using normal mode solutions to the Euler-Bernoulli problem for a cantilevered beam. These solutions are compared with motion of water and of the sedge Schoenoplectus americanus observed (using synchronized current meters and video) in a shallow salt marsh (depth < 1 m). Consistent with theory, sedge motion led water motion, with the phase decreasing (from 90 to 0 degrees) with increasing wave frequency. After tuning of a single free parameter (Young's modulus), the theory successfully predicted the transfer function between measured water and stem motion. Formulae predicting frequency-dependent wave dissipation by flexible vegetation are derived. For the moderately flexible stems observed, the model predicted total dissipation was about 30% of the dissipation for equivalent rigid stems. Copyright 2010 by the American Geophysical Union.