skip to main content

Title: Eulerian Two‐Phase Model Reveals the Importance of Wave Period in Ripple Evolution and Equilibrium Geometry

The evolution of ripple geometries and their equilibrium states due to different wave forcing parameters are investigated by a Reynolds‐averaged two‐phase model, SedFoam, in a two‐dimensional domain. 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.

more » « less
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
DOI PREFIX: 10.1029
Date Published:
Journal Name:
Journal of Geophysical Research: Earth Surface
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. A Reynolds-averaged two-phase Eulerian model for sediment transport, SedFoam, is utilized in a twodimensional domain for a given sediment grain size, flow period, and mobility number to study the asymmetric and skewed flow effects on the sediment transport over coarse-sand migrating ripples. First, the model is validated with a full-scale water tunnel experiment of orbital ripple driven by acceleration skewed (asymmetric) oscillatory flow with good agreement in the flow velocity, net sediment transport, and ripple migration rate. The model results showed that the asymmetric flow causes a net onshore sediment transport of both suspended and near-bed load (the conventional bed load and part of the near-bed suspended load, responsible for ripple migration). The suspended load transport is driven by the “positive phase-lag” effect, while the near-bed transport is due to the large erosion of the boundary layer on the stoss flank, sediment avalanching on the lee flank, and the returning flux induced by the stoss vortex. Together, these processes result in a net onshore transport rate. In contrast, for an energetic velocity skewed (skewed) flow, the net transport rate is offshore directed. This is due to a larger offshore-directed suspended load transport rate, resulting from the “negative phase-lag” effect, compared to the onshore-directed near-bed load transport rate. Compared to the asymmetric flow, the onshore near-bed load transport (and migration) rate is limited by the larger offshore directed flux associated with returning flow on the lee side, due to a stronger lee vortex generation during the onshore flow half-cycle. In the combined asymmetric-skewed case, the near-bed load and migration rate are higher than in the asymmetric flow case. Moreover, the offshore-directed suspended load is much smaller compared to the skewed flow case due to a competition between the negative (due to velocity skewness) and positive (due to acceleration skewness) phase-lag effects. As a result, the net transport rate is onshore directed but slightly smaller than the asymmetric flow case. 
    more » « less
  2. Abstract

    A new modeling methodology for ripple dynamics driven by oscillatory flows using a Eulerian two‐phase flow approach is presented in order to bridge the research gap between near‐bed sediment transport via ripple migration and suspended load transport dictated by ripple induced vortices. Reynolds‐averaged Eulerian two‐phase equations for fluid phase and sediment phase are solved in a two‐dimensional vertical domain with akεclosure for flow turbulence and particle stresses closures for short‐lived collision and enduring contact. The model can resolve full profiles of sediment transport without making conventional near‐bed load and suspended load assumptions. The model is validated with an oscillating tunnel experiment of orbital ripple driven by a Stokes second‐order (onshore velocity skewed) oscillatory flow with a good agreement in the flow velocity and sediment concentration. Although the suspended sediment concentration far from the ripple in the dilute region was underpredicted by the present model, the model predicts an onshore ripple migration rate that is in very good agreement with the measured value. Another orbital ripple case driven by symmetric sinusoidal oscillatory flow is also conducted to contrast the effect of velocity skewness. The model is able to 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 onshore flow cycle and sediment avalanching near the lee ripple flank which force the onshore ripple migration.

    more » « less
  3. Abstract

    Wave velocity and suspended sediment concentration were measured over a sand bed with and without a model eelgrass meadow. The model meadow was geometrically and dynamically similar to the marine eelgrassZostera marina. Meadows were constructed with three stem densities: 280, 600, and 820 stems/m2. Ripples formed within the meadow only when the spacing between stem rows was larger than the wave excursion. When ripples formed, the ripple geometry was the same as that observed for bare bed. When ripples were present, the near‐bed turbulent kinetic energy (TKE) was dominated by the ripple‐generated turbulence, and both the near‐bedTKEand averaged suspended sediment concentration were similar across all meadow densities and bare bed at the same wave velocity. When ripples were absent, the near‐bedTKEwas dominated by the stem‐generated turbulence, and the averaged suspended sediment concentration was reduced, compared to cases with ripples but at the same wave velocity. For conditions with and without a model meadow, the sediment diffusivity inferred from vertical profiles of suspended sediment concentration increased linearly with distance from the bed.

    more » « less
  4. Abstract

    We performed laboratory experiments to investigate the influence of sand content on the dynamics of wave‐supported gravity flows in mud‐dominant environments. The experiments were carried out in an oscillatory water tunnel with a sediment bed of either 1% or 13% sand. Low and high energy regimes are differentiated based on a Stokes Reynolds numberReΔ ≈ 500. In the low energy regime, the sand fraction influences flow dynamics primarily through ripple formation; no ripples form in the 1% sand experiments, whereas ripples form in the 13% experiments that increase turbulence and the wave boundary layer thickness,δm. In the high energy regime, small ripples form in both the 1% and 13% sand experiments and we observe high near‐bed suspended sediment concentrations. The influence of stratification on the boundary layer flow is characterized in terms of the gradient Richardson numberRig. The flow is weakly stratified inside the boundary layer for all runs and critically stratified at or above the top of the boundary layer. In the lower energy regime, the sand content reduces the relative influence of stratification in the boundary layer, shifting the elevation of critical stratification,LB, from approximately 1.3δmto 2.5δmin the 1% and 13% experiments, respectively. In both sets of experimentsLB ≈ δmat the strongest wave energy, indicating a transition to strongly stratified dynamics.

    more » « less
  5. Abstract

    The impacts of aquatic vegetation on bed load transport rate and bedform characteristics were quantified using flume measurements with model emergent vegetation. First, a model for predicting the turbulent kinetic energy,kt, in vegetated channels from channel average velocityUand vegetation volume fractionϕwas validated for mobile sediment beds. Second, using data from several studies, the predictedktwas shown to be a good predictor of bed load transport rate,Qs, allowingQsto be predicted fromUandϕfor vegetated channels. The control ofQsbyktwas explained by statistics of individual grain motion recorded by a camera, which showed that the number of sediment grains in motion per bed area was correlated withkt. Third, ripples were observed and characterized in channels with and without model vegetation. For low vegetation solid volume fraction (ϕ ≤ 0.012), the ripple wavelength was constrained by stem spacing. However, at higher vegetation solid volume fraction (ϕ=0.025), distinct ripples were not observed, suggesting a transition to sheet flow, which is sediment transport over a plane bed without the formation of bedforms. The fraction of the bed load flux carried by migrating ripples decreased with increasingϕ, again suggesting that vegetation facilitated the formation of sheet flow.

    more » « less