Two-phase modeling of sand ripple dynamics in oscillatory flow
Date
2022
Authors
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Publisher
University of Delaware
Abstract
Understanding the morphological behavior of the coastal regions and predicting the coastal changes in response to climate change and human activities have been the centerpiece in the coastal engineering. These morphological changes are the result of the complex coupling between hydrodynamics and sediment transport which happens in different spatial and temporal scales. Among them, sediment transport above migrating sand ripples has drawn many researchers’ attention for more than a century. However, several research gaps still exist. In this study, an Eulerian two-phase flow model, SedFoam is utilized to bridge these research gaps. In this study, Reynolds-Averaged Eulerian two-phase equations for fluid phase and sediment phase are solved in a two-dimensional vertical domain with a k- closure for flow turbulence and particle stresses closures for short-lived particle collision and enduring contact. As a result, SedFoam can resolve full profiles of sediment transport without making conventional near-bed load and suspended load assumptions. ☐ As a first step, SedFoam has been validated with an oscillating tunnel experiment of orbital ripple driven by a Stokes 2nd-order (onshore velocity skewed) oscillatory flow and shows a good agreement with the measured flow velocity and sediment concentration. Although the suspended sediment concentration far from the ripple in the dilute region was under-predicted by the present model, the model predicts an onshore ripple migration rate that is in very good agreement with the measured value. The model can capture a net offshore-directed suspended load transport flux due to the asymmetric primary vortex consistent with laboratory observation. More importantly, the model can resolve the asymmetry of onshore-directed near-bed sediment flux associated with more intense boundary layer flow speed-up during the onshore flow cycle and sediment avalanching near the lee ripple flank which forces the onshore ripple migration. ☐ SedFoam was further utilized to investigate the evolution of ripple geometries and their equilibrium states due to different wave forcing conditions. Modeled ripple geometries, for a given uniform grain diameter, show a good agreement with ripple predictors that include the wave period effect explicitly, in addition to the wave orbital excursion length (or wave orbital velocity amplitude). Furthermore, using a series of numerical experiments, the ripple’s response to a step-change in the wave forcing is studied. The model is capable of simulating “splitting”, “sliding”, “merging”, and “protruding” as the ripples evolve to a new equilibrium state. The model can also simulate the transition to sheet flow in energetic wave conditions and ripple reformation from a nearly flat bed condition. Simulation results reveal that the equilibrium state is such that the “primary” vortices reach half of the ripple length. Furthermore, an analysis of the suspended load and near-bed load ratio in the equilibrium state indicates that in the orbital ripple regime, the near-bed load is dominant while the suspended load is conducive to the ripple decaying regime (suborbital ripples) and sheet flow condition. These important findings are further used to explain the importance of wave period in determining the equilibrium ripple geometry. ☐ Finally, for a given sediment grain size, flow period, and mobility number, the velocity skewness and/or acceleration asymmetry effect on the sediment transport over migrating coarse sand ripples has been investigated. SedFoam results showed that the acceleration asymmetry drives a net onshore-directed suspended load transport through the “positive phase-lag” effect and a net onshore-directed near-bed load transport. Collectively, a net onshore transport rate is obtained. Contrarily, in the case of velocity-skewed flow in high wave energy, the net offshore directed transport rate results from an offshore directed suspended transport rate (due to the “negative phase-lag” effect) larger than the onshore directed near-bed load transport rate. Compared to the acceleration-asymmetric case, the onshore near-bed load transport (and migration) rate is limited by the larger offshore directed flux associated with returning flow of primary vortex on the lee side, due to a stronger lee vortex generation during the onshore flow half-cycle. In the combined skewed-asymmetric case, the near-bed load and migration rate are even higher than the acceleration-asymmetric case. The suspended load is much less offshore directed compared to the velocity-skewed case due to a competition between negative (due to velocity skewness) and positive (due to acceleration asymmetry) phase-lag effects. As a result, the net transport rate is slightly smaller than the asymmetric case. ☐ The present study has established the capability of SedFoam to simulate wave-driven ripples using the Reynolds-averaged approach. Future work will focus on 3D simulation of sand ripple dynamics using SedFoam with Large-Eddy Simulation (LES) methodology for better resolving the flow coherent structures and their effects on the ripple formation, migration, and evolution. Future applications of SedFoam can also be involved in some ecological studies aimed to investigate the benthic flux exchange over migrating ripples.
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Keywords
Coastal engineering, SedFoam, Coastal changes, Hydrodynamics, Sediment transport