Seagrass blade dynamics were explored through numerical and laboratory experiments in order to improve parameterization of wave attenuation by submerged aquatic vegetation in the presence of a background current. In the numerical model, a single blade was modeled as a series of rigid plates attached by torsion springs. For the laboratory model, strips of low‐density polyethylene were placed in a recirculating wave flume. A new form of the Keulegan—Carpenter number based on the horizontal excursion of the blade tip was found to be an excellent predictor of drag coefficient. An algebraic model for predicting wave attenuation was developed based on the following observations. During the portion of the wave period when the fluid velocities are highest, the blade motion is almost completely arrested and the vast majority of the turbulence production occurs during this time. Turbulence production when the blade is pronated is accurately predicted by the maximum fluid velocity over the wave period. The relative contribution to the total turbulence production over the wave period is determined by the relative strength of the waves and the current. Therefore, using a simple algebraic fit, the total depth‐integrated, time‐averaged turbulence production can be accurately predicted by two flow parameters: the maximum fluid velocity over the wave period, and a non‐dimensional number that compares the wave and current velocities. By fitting the algebraic model to data from a particular site, it can be used to efficiently estimate wave attenuation and drag coefficient in seagrass exposed to waves with a background current.
Laboratory experiments were used to evaluate and improve modelling of combined wave-current flow through submerged aquatic canopies. Horizontal in-canopy particle image velocimetry (PIV) and wavemaker-measurement synchronization allowed direct volume averaging and ensemble averaging by wave phase, which were used to fully resolve the volume-averaged unsteady momentum budget. Parameterizations for the drag, Reynolds stress, vertical advection, wake production and shear production were tested against the laboratory measurements. The drag was found to have small errors due to unsteadiness and the finite aspect ratio of the canopy elements. The Smagorinsky model for the Reynolds stress showed much better agreement with the measurements than the quadratic friction parameterization used in the literature. A proposed parameterization for the vertical advection based on linear wave theory was also found to be effective and is much more computationally efficient than solving the pressure Poisson equation. A simple 1D 0-equation Reynolds-averaged Navier-Stokes (RANS) model was developed to use these parameterizations. The basic framework of the model is an extrapolation from previous 2-and 3-box models to N boxes. While the resolution of the model is flexible, the filter length for the Smagorinsky parameterization has to be chosen appropriately. With the proper filter length, the N-box model demonstrated good agreement with the measurements at both low and high resolution. Scaling analysis was used to establish a region of parameter space where the N-box model is expected to be effective. The following conditions define this region: the wave-induced velocity is of similar or greater magnitude than the background current, the drag to shear length ratio is small enough to produce canopy behaviour, the wave orbital excursion is not much larger than the drag length, the Froude number is small and the canopy is under shallow submergence, yet far from emergent. Under these assumptions, the dominant balance is between pressure and unsteadiness, the drag is secondary, and the other terms are small. The simple Reynolds stress parameterization in the N-box model is appropriate under these conditions because the Reynolds stress is unlikely to be the dominant source of error. This finding is important because the Reynolds stress is typically one of the dominant drivers of computational cost and model complexity. Based on these findings, the N-box model is expected to be a practical tool for a wide range of combined wave-current canopy flows because of its simplicity and computational efficiency.
Although shear layers generated by submerged vegetation reach a steady state once production and dissipation are balanced within a canopy, shear layers found in gaps and after trailing edges of canopy patches are inherently different and thereby perturb the canopy's mean and turbulent fields. Experiments were conducted in a laboratory flume to study canopy systems in which two model patches of submerged, rigid cylinder arrays are interrupted by a gap of varying stream‐wise lengths. Results show that, consistent with past studies, gaps locally enhance turbulence. However, this perturbation does not remain “local” within the gap, instead introducing enhanced turbulent energies throughout the water column that are transported downstream and thereby perturb the canopy flow. The study suggests a scaling, E=H−hcqU2L2, which compares the eddy turnover time of the turbulence produced by the gap to the advection time downstream the second patch, that can be used to predict if turbulence perturbations induced by an upstream gap will influence the turbulence at a given distance downstream.
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