A simple and practical model for combined wave–current canopy flows

Abstract

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.

The attenuation of current‐ and wave‐driven flow within submerged multispecific vegetative canopies

“…Moreover, the present model has no explicit accommodations for wave‐current and flow‐element interactions. Both these mechanisms have been shown to have considerable influence over mean canopy hydrodynamics (Luhar and Nepf ; Zeller et al ; Zeller et al). Although the experiments in this study were not designed to account for these interactions, their investigation—especially in such complex conditions—should be kept as a top priority.…”

“…Data processing schemes like the one described above are unable to overcome the fundamental challenge of data paucity. For that, we have begun a transition toward data collection via particle image velocimetry, an approach that yields far richer velocity field information (Weitzman et al ; Zeller et al ; Zeller et al). This will allow us to characterize the horizontal variability of flow statistics and develop new methods for interpreting sparse measurements…”

Sediment transport in the presence of large reef bottom roughness

“…Laboratory experiments with idealized canopies [e.g., Lowe et al ., ; Luhar et al ., ] and field experiments in seagrass canopies [e.g., Infantes et al ., ] have demonstrated that the attenuation of the root‐mean‐squared (RMS) wave orbital velocities within the canopy is always less than that of a unidirectional flow of equivalent magnitude. This is due to the wave‐driven oscillatory pressure gradient, which is opposed by both canopy drag and inertial forces [e.g., Lowe et al ., ; Zeller et al ., ]. Furthermore, wave phase‐dependent Reynolds stresses are enhanced near the top of the roughness and then decrease toward zero within the canopy before they increase again near the bed [e.g., Lowe et al ., ; Luhar et al ., ].…”

“…The dynamics of wave‐current interactions that occur within large roughness (canopies) are still not well‐established. However, it is reasonable to assume that the drag imposed by large roughness elements will cause greater attenuation of the current‐component of the flow relative to the wave‐component, which is supported by experimental observations [e.g., Lowe et al ., ; Zeller et al ., ]. Thus, under wave‐current conditions the flow within the roughness should be more strongly influenced by the contribution of the waves than the current.…”

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

“…Meanwhile, the wave‐driven currents and wave asymmetry also influence the asymmetry of blade motion. It is therefore worthwhile not only to investigate the dynamics of vegetation, but to also incorporate the two‐way feedback between the asymmetric blade motion and the wave flow field in wave‐vegetation models, such as the coupled CFD and immersed boundary method model by Chen and Zou () and N‐box model (Zeller et al, ). Improved blade posture simulations by the present consistent‐mass cable model will yield more accurate predictions for wave‐vegetation interaction.…”