Wave-induced dynamics of flexible blades

Abstract

We present an experimental and numerical study that describes the motion of flexible blades, scaled to be dynamically similar to natural aquatic vegetation, forced by wave-induced oscillatory flows. For the conditions tested, blade motion is governed primarily by two dimensionless variables: (i) the Cauchy number, $Ca$, which represents the ratio of the hydrodynamic forcing to the restoring force due to blade stiffness, and (ii) the ratio of the blade length to the wave orbital excursion, $L$. For flexible blades with $Ca \gg 1$, the relationship between drag and velocity can be described by two different scaling laws at the large- and small-excursion limits. For large excursions ($L \ll 1$), the flow resembles a unidirectional current and the scaling laws developed for steady-flow reconfiguration studies hold. For small excursions ($L \gg 1$), the beam equations may be linearized and a different scaling law for drag applies. The experimental force measurements suggest that the small-excursion scaling applies even for intermediate cases with $L \sim O(1)$. The numerical model employs the well-known Morison force formulation, and adequately reproduces the observed blade dynamics and measured hydrodynamic forces without the use of any fitted parameters. For $Ca \gg 1$, the movement of the flexible blades reduces the measured and modeled hydrodynamic drag relative to a rigid blade of the same morphology. However, in some cases with $Ca \sim O(1)$, the measured hydrodynamic forces generated by the flexible blades exceed those generated by rigid blades, but this is not reproduced in the model. Observations of blade motion suggest that this unusual behavior is related to an unsteady vortex shedding event, which the simple numerical model cannot reproduce. Finally, we also discuss implications for the modeling of wave energy dissipation over canopies of natural aquatic vegetation.