Wave-induced dynamics of flexible blades

Abstract

In this paper, 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 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 1), the flow resembles a unidirectional current and the scaling laws developed for steady-flow reconfiguration studies hold. For small excursions (L 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 ∼ 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 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 ∼ 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.

Drag measurements in laterally confined 2D canopies: Reconfiguration and sheltering effect

“…Recent investigations also explore various mechanically activated phenomena in plants or plant canopies that arise from interaction between the fluid flow (air or water) and vegetation. 19 For example, flow-induced vibration and the origin of coherent structures on crop canopies, [20][21][22][23] dissipation of wave energy, 24,25 population growth and ecological consequences, 26 flow-triggered pruning, 27 and seed-dispersal 28,29 were studied. For many such investigations, one of the key ingredients in the analysis is the drag force experienced by a canopy, a plant, and its parts.…”

Mechanisms for the Asymmetric Motion of Submerged Aquatic Vegetation in Waves: A Consistent‐Mass Cable Model

“…For simplicity, Zeller et al () selected an approximated value of 0.02. In contrast, Luhar and Nepf () used a larger value of because their model was found unstable for the cases with high Cauchy number if . The Cauchy number ( Ca ) is the ratio of the hydrodynamic force to the restoring force due to plant stiffness and given by .…”

“…The velocity profile was measured using particle image velocimetry (PIV, details referred to Luhar & Nepf, ) that captures the instantaneous flow velocity resulting from the superposition of the incident and reflected waves, where the wave reflection ratio of the wave flume is 7% (Lei & Nepf, ). The first four harmonics fit of the measured flow velocity ( , Figure ) at one horizontal position was used as an approximation for the input flow field in Luhar and Nepf (). This approximation only represents the temporal variation of the velocity profile at that horizontal position.…”

“…Measured horizontal component of the wave orbital velocity at = 0 for the wave with period = 2 s and amplitude = 4 cm (Luhar & Nepf, ). The measured horizontal component of the wave orbital velocity is denoted by the dotted black line, and the first four harmonics fit is denoted by solid green line.…”

Linking social, ecological, and physical science to advance natural and nature‐based protection for coastal communities

“…In general, the protective services provided by coastal ecosystems can be classified as hydrodynamic and sedimentary processes. The most commonly reported indicators of coastal protection are hydrodynamic proxies, particularly those relating to attenuation of wave height and reduction of flow velocity . The prevailing focus on hydrodynamics is due, at least in part, to the dependence of other important phenomena (such as sediment transport and soil erosion) on accurate predictions of hydrodynamic forces at various spatial and temporal scales.…”