Three‐dimensional mixture simulations of flow over dynamic rippled beds

Abstract

[1] A three-dimensional mixture theory model for flow and sediment transport in the seafloor boundary layer, SedMix3D, simulated the flow over and the resulting sediment entrainment and evolution of rippled beds. SedMix3D treats the fluid-sediment mixture as a continuum of varying density and viscosity with the concentration of sediment and velocity of the mixture simulated by the Navier-Stokes equations coupled with a sediment flux equation for the mixture. Model validation was performed by comparing simulated time-dependent flow quantities and bulk flow statistics with measurements obtained in the laboratory under scaled forcing conditions. Two-dimensional planes extracted from a three-dimensional simulation were compared to observations made using planar Particle Image Velocimetry (PIV) in a laboratory flume. The simulated results of time-averaged velocities and time-dependent quantities of vorticity and swirling strength were in good agreement with the observations. The model was used to analyze the three-dimensionality of vortex formation and ejection produced by oscillatory flow over vortex ripples, a process that cannot be observed in the laboratory with planar PIV measurements. The three-dimensional simulated results showed that the swirling strength varied significantly in the cross-flow direction, indicating that the vortices formed and dissipated non-uniformly due to random fluctuations. Subsequently, an order of magnitude difference in offshore sediment flux was observed using two different methods to calculate sediment fluxes (spatially averaging and at a point). The results suggest that while a two-dimensional plane may be sufficient to examine the general hydrodynamics over ripples, three-dimensional analysis is necessary for a complete understanding of sediment transport.

Unsteady stress partitioning and momentum transfer in the wave bottom boundary layer over movable rippled beds

“…Using a three‐dimensional mixture model, Penko et al . [] showed that for the present experimental conditions vortices formed and dissipated nonuniformly in the cross‐flow direction due to random fluctuations, yet swirling strength comparisons were generally favorable. Although turbulent intensities measured in this effort are fairly consistent with previous studies (see section 4.1), we anticipate that the effects of three‐dimensionality may influence the Reynolds stress estimates, which accounts for ∼20% of the total RMS stress (section 4.4).…”

“…A phase lead of , computed with cross‐correlation analysis, is present at the lower 0.7 cm of the water column, consistent with the numerical effort of Penko et al . [], and previous laboratory [ van der Dominic et al ., ], and field [ Foster et al ., ] observations over a flat bed. Figure a shows that in general, is ∼O(10) times larger than .…”

“…The location and timing of these vortical structures have been qualitatively validated with the numerical effort of Penko et al . [].…”

Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer

“…However, at the Reynolds numbers involved in the experiments, the turbulent structure of the flow and its interaction with the sediment are known to be highly three-dimensional (Ozdemir et al 2010;Penko et al 2013). Of particular importance are the three-dimensional vortical structures which provide the regions of upward directed flow necessary for sediment to travel away from the bed and remain in suspension.…”

Nearshore dynamics of artificial sand and oil agglomerates

“…Models capable of resolving fine-scale hydrodynamics and sediment transport within the WBBL include ReynoldsAveraged Navier-Stokes (RANS) models (e.g., Winterwerp, 2001;Bakhtyar et al, 2009;Hsu et al, 2009); Large-Eddy Simulation (LES) models (e.g., Zedler and Street, 2001;Chang and Scotti, 2004;Harris and Grilli, 2012); and Direct Numerical Simulation (DNS), which resolves all scales of turbulent flow without the use of a closure model (e.g., Bhaganagar and Hsu, 2009;Ozedmir et al, 2010). Recent advancements have also included capturing the feedback between sediment and fluid within the WBBL, such as utilizing mixture theory within unfiltered Navier-Stokes equations to capture sand ripple dynamics (Penko et al, 2011(Penko et al, , 2013. Models for resolving the motion of cm-sized particles such as SOAs or cobbles have been developed using balance-of-force approaches assuming the particle is driven primarily by the freestream flow, neglecting influences of the WBBL (e.g., Voropayev et al, 1998Voropayev et al, , 2001, but these models do not capture interactions with bed forms.…”