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Coastal Engineering A numerical study of sheet flow driven by velocity and acceleration skewed nearbreaking waves on a...
A numerical study of sheet flow driven by velocity and acceleration skewed nearbreaking waves on a sandbar using SedWaveFoam
Kim, Yeulwoo, Mieras, Ryan S., Cheng, Zhen, Anderson, Dylan, Hsu, TianJian, Puleo, Jack A., Cox, DanielQuanto Você gostou deste livro?
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english
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Coastal Engineering
DOI:
10.1016/j.coastaleng.2019.103526
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July, 2019
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Accepted Manuscript A numerical study of sheet flow driven by velocity and acceleration skewed nearbreaking waves on a sandbar using SedWaveFoam Yeulwoo Kim, Ryan S. Mieras, Zhen Cheng, Dylan Anderson, TianJian Hsu, Jack A. Puleo, Daniel Cox PII: S03783839(19)300626 DOI: https://doi.org/10.1016/j.coastaleng.2019.103526 Article Number: 103526 Reference: CENG 103526 To appear in: Coastal Engineering Received Date: 15 February 2019 Revised Date: 16 June 2019 Accepted Date: 7 July 2019 Please cite this article as: Kim, Y., Mieras, R.S., Cheng, Z., Anderson, D., Hsu, T.J., Puleo, J.A., Cox, D., A numerical study of sheet flow driven by velocity and acceleration skewed nearbreaking waves on a sandbar using SedWaveFoam, Coastal Engineering (2019), doi: https://doi.org/10.1016/ j.coastaleng.2019.103526. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering A numerical study of sheet flow driven by velocity and acceleration skewed nearbreaking waves on a sandbar using SedWaveFoam 1 2 3 10 11 12 Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, Delaware, USA 2 National Research Council, Postdoctoral Research Associate, Research Associateship Program, Marine Geosciences Division, U.S. Naval Research Laboratory, Stennis Space Center, MS, USA 3 SC 8 9 1 Convergent Science Inc., Madison, WI, USA 4 Coastal and Ocean Engineering Program, School of Civil and Construction Engineering, Oregon State University, Corvallis, OR, USA M AN U 6 7 RI PT ; Yeulwoo Kim1, Ryan S. Mieras2, Zhen Cheng3, Dylan Anderson4, TianJian Hsu1, Jack A. Puleo1, and Daniel Cox4 4 5 13 Corresponding author: Y. Kim (ykim@udel.edu) 15 16 Keywords: Sediment transport; Sheet flow; Momentary bed failure; Twophase model; Progressive Wave Streaming; Wavestirring effect AC C EP TE D 14 1 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering Abstract 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 A new methodology capable of concurrently resolving free surface wave field, bottom boundary layer, and sediment transport processes throughout the entire water column was recently developed in the OpenFOAM framework, called SedWaveFoam. In this study, SedWaveFoam is validated with large wave flume data for sheet flow driven by nearbreaking waves. Good agreements are obtained for free surface elevation, flow velocity, turbulence kinetic energy, sediment concentration, and sheet flow sediment fluxes. Model results are used to investigate the joint effects of velocity skewness, acceleration skewness, and progressive wave streaming on sheet flow sediment transport. SedWaveFoam results are contrasted with rigidlid onedimensionalvertical model results to isolate the effect of the free surface. Onshore directed nearbed flow velocity and sediment flux are enhanced due to the presence of the free surface via progressive wave streaming. However, the enhancement of net onshore sediment transport for the nearbreaking condition with both high velocity and acceleration skewness is several factors greater than that found in the nonbreaking condition with only high velocity skewness. Model results suggest that the large horizontal pressure gradient, which has a Sleath parameter exceeding 0.2, may play a key role. Momentary bed failure is identified via nearbed instability of the sheet flow layer, associated with a large bed shear stress and horizontal pressure gradient. Instantaneous nearbed vortices due to the nearbed instability correspond to the increase of horizontal pore pressure gradient during the wave crest, consistent with measured data. Model intercomparison suggests that a twodimensional model is crucial to capture the effect of momentary bed failure that increases sediment suspension during wave crest passage and net onshore sediment transport. AC C EP TE D M AN U SC RI PT 17 2 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 39 1. Introduction Sandbars are prominent nearshore bathymetric features where sediment transport and 41 rapid morphological change can occur [Thornton et al., 1996; Gallagher et al., 1998; Aagaard et 42 al., 2002; Ruggiero et al., 2005; Ruessink et al., 2009; Tissier et al., 2011; Grasso et al., 2012]. 43 Sandbars enhance depthinduced wave breaking and help determine the crossshore evolution of 44 wave shape and crossshore and alongshore currents [Reniers et al., 2004], altering sediment 45 transport patterns. Therefore, improved prediction of coastal morphological evolution is closely 46 related to the understanding of onshore and offshore sediment fluxes driven by waves and 47 currents that lead to crossshore sandbar migration [Henderson et al., 2004; Hsu et al., 2006; 48 Ruessink and Kuriyama, 2008; FernándezMora et al., 2015]. However, a comprehensive 49 understanding of sediment transport under surface waves does not yet exist due to many inter 50 connected mechanisms and uncertainties in their relative importance, such as: velocity skewness 51 [Doering et al., 2000; Austin et al., 2009; Cheng et al., 2017]; progressive wave streaming 52 [Nielsen, 2006; Holmedal and Myrhaug, 2009, Kranenburg et al., 2012, 2013; Fuhrman et al., 53 2013; Kim et al., 2018]; acceleration skewness [Drake and Calantoni, 2001; Foster et al., 2006]; 54 and wavebreaking turbulence [Voulgaris and Collins, 2000; Scott et al., 2009; Aagaard and 55 Hughes, 2010; Yoon and Cox, 2010]. SC M AN U TE D EP The significance of progressive wave streaming in driving onshore sediment transport for AC C 56 RI PT 40 57 various grain sizes and wave conditions has been identified and quantified using 1DV boundary 58 layer sediment transport models employing the relationship of 59 Holmedal and Myrhaug, 2009; Fuhrman et al., 2013], in which 60 an opensource free surface resolving Eulerian twophase sediment transport model, 61 SedWaveFoam [Kim et al., 2018], was developed by combining two numerical models, 62 SedFoam [Cheng et al., 2017] and InterFoam/waves2Foam [Berberović et al., 2009; 3 ⁄ = −1 ⁄ [e.g., is the wave celerity. Recently, ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering Klostermann et al., 2012/Jacobsen et al., 2012], using the OpenFOAM CFD toolbox. By its 64 design, SedWaveFoam concurrently resolves the free surface wave field, bottom boundary layer, 65 and sediment transport processes throughout the entire water column. Kim et al. [2018] reported 66 detailed model formulation of SedWaveFoam and its validation with a large wave flume 67 experiment for sheet flow driven by monochromatic nonbreaking waves [DohmenJanssen and 68 Hanes, 2002]. Additional onedimensionalvertical (1DV) SedFoam simulations (similar to an 69 oscillating water tunnel [OWT] without a free surface) were conducted. Comparison of model 70 results shows progressive wave streaming enhances onshore sediment transport driven by 71 velocity skewness by about 60% for median sand grain size of 0.24 mm and velocity skewness 72 of 0.39 (see more information in Section 4.1) that may be explained using a wavestirring 73 concept [Kim et al., 2018]. M AN U SC RI PT 63 Sediment transport in the vicinity of a sandbar where waves shoals and break is more 75 complicated due to the combined effects of wave velocity skewness, progressive wave 76 streaming, and horizontal pressure gradient. The horizontal pressure gradient is important for 77 sediment mobilization [Madsen, 1974; Sleath, 1999; Foster et al., 2006; Frank et al., 2015b] and 78 many numerical and laboratory studies have attempted to quantify onshore sediment transport 79 amplified by horizontal pressure gradient (or acceleration skewness) using an idealized saw 80 tooth wave shape [Drake and Calantoni, 2001; Hsu and Hanes, 2004; van der A et al., 2013]. The 81 Sleath parameter, 82 stabilizing forces (gravity) [Sleath, 1999]. Plug flow (or momentary bed failure) was observed in 83 OWT experiments when 84 threshold value of the magnitude of 85 due to the combined effect of large bed shear stress and horizontal pressure gradient [Frank et al., AC C EP TE D 74 , is a ratio between the destabilizing (horizontal pressure gradient) and was greater than 0.3. However, field observations showed that the can be as low as 0.1 in the surf zone [Foster et al., 2006], 4 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 86 2015a]. Cheng et al. [2017] confirm, using SedFoam, that large bed shear stress combined with 87 large horizontal pressure gradients can trigger instabilities of the sheet flow layer and cause 88 momentary bed failure which lowers the resulting critical 89 demonstrated the importance of horizontal pressure gradient (or acceleration) in driving onshore 90 sediment transport. However, most of the studies did not include free surface effects [Drake and 91 Calantoni, 2001; Hsu and Hanes, 2004; van der A et al., 2013]. Full vertical profiles of cross 92 shore sediment transport under free surface waves can be simulated using SedWaveFoam, which 93 allows more complete evaluation of the combined effects of progressive wave streaming, 94 velocity skewness, and accelerationskewness under nearbreaking waves. M AN U SC RI PT . The aforementioned studies Sheet flow is the transport of a sediment layer with high concentration, typically driven 96 by large bed shear stress. A near prototypescale sandBAR SEDiment transport experiment 97 (BARSED) was conducted in the large wave flume of O. H. Hinsdale Wave Research Laboratory 98 at Oregon State University [Anderson et al., 2017; Mieras et al., 2017, 2019] to understand sheet 99 flow dynamics driven by skewedasymmetric surface waves over a fixed sandbar containing a 100 sediment pit on the sandbar crest. Instantaneous highresolution sediment concentration profiles, 101 pore pressure gradients, and nearbed velocity profiles were measured concurrently (see Section 102 3 for more details). Maximum sheet flow layer thickness was wellcorrelated with maximum bed 103 shear stress [Mieras et al., 2017]. Suspended load and bed load sediment transport processes 104 were quantified under a range of wave conditions with varying degrees of skewness and 105 asymmetry [Mieras et al., 2019]. Particularly, the measured horizontal pore pressure gradients 106 were greater for larger acceleration skewness, and the horizontal pore pressure gradient may not 107 be equal to the local acceleration under strongly asymmetric surface waves [Mieras et al., 2017; 108 Anderson et al., 2017]. Sediment mobilization via momentary bed failure occurred presumably AC C EP TE D 95 5 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering due to the combined effect of large bed shear stress preceded by strong horizontal pressure 110 gradients at flow reversal. However, flow velocity profiles within the sheet flow layer were not 111 directly measured during BARSED, and further investigation through numerical modeling 112 efforts is needed to understand the physical processes driving sheet flow dynamics under 113 skewedasymmetric surface waves. RI PT 109 The purpose of this study is to investigate the physical mechanisms driving sediment 115 transport using the new numerical modeling strategy for skewedasymmetric surface waves. 116 SedWaveFoam is applied to simulate sheet flow driven by nearbreaking waves on the sandbar 117 crest during the BARSED experiment [Anderson et al., 2017; Mieras et al., 2017, 2019]. Model 118 formulations are discussed in Section 2. Section 3 presents the main model results including a 119 comprehensive model validation of flow and sediment transport characteristics. Section 4 is 120 devoted to discussion on the combined effects of progressive wave streaming, velocity skewness, 121 and acceleration skewness. Lastly, the main conclusions of this study are summarized in Section 122 5. TE D M AN U SC 114 124 EP 123 2. Numerical models This study uses two numerical models: SedWaveFoam [Kim et al., 2018]; and SedFoam 126 [Cheng et al., 2017]. SedWaveFoam is able to concurrently resolve the surface wave field, 127 bottom boundary layer, and sediment transport processes. SedFoam has essentially the same 128 capabilities as SedWaveFoam in modeling sediment transport based on a twophase flow 129 formulation. In contrast to SedWaveFoam, however, SedFoam is only able to account for the 130 sediment and water phases, thus it is incapable of resolving the free surface. Hence, 131 SedWaveFoam is the primary model used in this study to investigate sheet flow driven by near AC C 125 6 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 132 breaking waves. Free surface effects on sediment transport are isolated by comparing results 133 from the SedWaveFoam model with SedFoam results. 2.1 Governing equations 135 A brief description of the numerical model is provided here with more details given 136 elsewhere [Cheng et al., 2017; Kim, 2018; Kim et al., 2018]. A Reynoldsaveraged approach is 137 adopted to avoid resolving 3D turbulence covering a wide range of scales. The Reynolds 138 averaged mass conservation equations for three phases (air, water, and sediment) are written as 139 [e.g., Drew, 1983; Berberović et al., 2009] M AN U SC RI PT 134 140 ∂φ a ∂φ a uia + = 0, ∂t ∂xi (1) 142 ∂φ w ∂φ wuiw + = 0, ∂t ∂xi (2) TE D 141 ∂φ s ∂φ s uis + = 0, ∂t ∂xi 143 EP 144 (3) where i = 1, 2 for the present twodimensionalvertical (2DV) flows and the superscripts , 146 and 147 volumetric concentration of each phase where the total mass conservation requires 148 AC C 145 represent air, water, and sediment phases, respectively. The variable = 1. The variable , stands for the + + represents the velocity of each phase. The air and water (fluid) phases 149 are considered to be two immiscible fluids, and they are combined as the airwater mixture phase 150 [Kim et al., 2018]. Adopting the airwater interface tracking strategy of InterFoam [Berberović et 7 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 151 al., 2009; Klostermann et al., 2012], the mass conservation equation of airwater mixture phase is 152 expressed as a w r f ∂ φ w ∂ φ w u i f ∂ (φ φ u i φ + + ∂t ∂ xi ∂ xi 154 ) = 0, (4) SC 155 RI PT 153 where the relative velocity between the air and water phases, 157 the interface compression method to minimize numerical diffusion at the interface [Berberović et 158 al., 2009; Klostermann et al., 2012]. The superscript “ ” stands for the mixture of air and water 159 (fluid) phases where 160 incorporated and only Eq. (2) and (3) are considered. The sediment (solid) phase is considered to 161 be miscible with the airwater mixture (fluid) phase. Thus, the term “twophase” henceforth 162 refers to two miscible phases which are the airwater mixture (fluid) and sediment (solid) phases. 163 The dynamics of both phases can be resolved by the Eulerian twophase mass and momentum 164 equations appropriate for sediment transport [Dong and Zhang, 1999; Li et al., 2008; Cheng et al. 165 2017]. The Reynoldsaveraged momentum equations for the present airwater mixture and 166 sediment phases are written as [e.g., Kim et al., 2018] 168 169 and = + / . In SedFoam, Eq. (4) is not EP TE D = AC C 167 + , is obtained by iteration using M AN U 156 f f f f f ∂ρ f φ f ui f ∂ρ φ ui u j ∂p f ∂φ a ∂ τ ij + = −φ f + ρ f φ f gδ i 2 − σ t γ + + M i fs , ∂t ∂x j ∂ xi ∂ xi ∂x j (5) s s s s ∂τ s ∂ρ sφ s uis ∂ρ φ ui u j ∂p f ∂p s + = −φ s − + ρ sφ s gδ i 2 + ij + M isf , ∂t ∂x j ∂xi ∂xi ∂x j (6) 170 8 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 171 172 where = is the sediment density (= 2,650 kg/m3). The mixture fluid density, + / , in which = 1 kg/m and , is calculated as = 1000 kg/m here. The variable ! is the fluid pressure, and g = −9.8 m/s & is gravitational acceleration. Since the free surface 174 evolution is resolved, the effect of surface tension is included in the third term on the righthand 175 side (RHS) of Eq. (5) where ' is the surface curvature. The surface tension coefficient () is 176 RI PT 173 specified as () = 0.074 kg/s & representing the airwater interface at the temperature of 20℃ . The fluid stress, . / , consists of grainscale viscous stress and turbulent Reynolds stress with the 178 latter calculated by a twoequation kε turbulence model for twophase flow (see Section 2.2.1). 179 The particle pressure, ! , and particle shear stress, . / , are modeled with the kinetic theory of 180 granular flow for particle collision at low to moderate concentration and phenomenological 181 closures for enduring contact at high sediment concentration (see Section 2.2.2, and Cheng et al., 182 2017 for more details). The interphase momentum transfer between the fluid and sediment 183 phases follows Newton’s 3rd law, 0 184 averaged mean velocity difference and turbulent suspension as M AN U SC 177 188 TE D which consists of drag force due to Reynolds M i fs = −φ s β ( uif − uis ) + β AC C 187 EP 185 186 = −0 ν ft ∂φ s , σ c ∂xi where 1 is the drag parameter [Ding and Gidaspow, 1990], 2 ) (7) is the turbulent viscosity of the 189 fluid phase, and (3 = 1.0 is the Schmidt number. More detailed formulation can be found in 190 Cheng et al. [2017]. 191 9 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 192 2.2 Closures 193 2.2.1 Fluid turbulence closures 194 Fluid stresses, . / , in Eq. (5) consist of turbulent Reynolds stress, 4 / , and grainscale viscous stress, 5 / which can be written as 196 2 + 2 / + M AN U in which the kinematic viscosity of carrier fluid (i.e., airwater mixture) is defined as 2 = 200 where 2 = 1.48 × 1078 m& /s and 2 = 1079 m& /s . The turbulent eddy viscosity, 2 ) , is calculated by turbulent kinetic energy (TKE), : , and 202 turbulent dissipation rate, ; , as 2 203 0.09 ). The deviatoric part of the strain rate of mixture fluid phase, 206 207 B ?@A ?CD + B ?@D ?CA E− B = ?@F ?CF G /. < : & /; where < is an empirical coefficient ( TE D & > = /, is defined as < = / = EP 205 = ) The balance equation for TKE is written as [Kim et al., 2018] AC C 204 (8) SC 2 3 198 201 τ ijf = Rijft + rijf = ρ f φ f 2 (ν ft +ν f ) Sijf − k f δij , 197 199 RI PT 195 ) f f f ∂u f ∂ρ f k f ∂ρ u j k ∂ f f ν ft ∂k f + = Rijft i + ρ ν + ∂t ∂x j ∂x j ∂x j σ k ∂x j , 2 β (1 − α ) φ s k f ρ f ν ft ∂φ s f f −ρ ε − − f ( s − 1) gδ j 3 φf φ σ c ∂x j 208 10 (9) ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 209 where (H = 1.0 is the Schmidt number for TKE [Rodi, 1993], and / 210 gravity of sediment. The TKE attenuation due to particle inertia effects is included in the fourth 211 term on the RHS of Eq. (9) following Cheng et al. [2017]. Particularly, the level of correlation 212 between fluid and sediment velocity fluctuations is modeled as I = exp −M is the specific ) following RI PT = 213 Danon et al. [1977] and Chen and Wood [1985], in which M = 0.16 is an empirical coefficient 214 and 215 energetic eddies. The buoyancy effect caused by density stratification is also included in the last 216 term of Eq. (9). For sediment transport, this term usually contributes as an attenuation term of 217 TKE due to stable density stratification. Similarly, the balance equation for turbulence dissipation rate is written as 219 TE D 221 f f f f ∂ρ f ε f ∂ρ u j ε ∂ f f ν ft ∂ε f ε f ∂u i f f ε + = C1ε Rijft f + − C ρ εf ρ ν + 2ε ∂t ∂x j k ∂x j ∂x j σ ε ∂x j kf , s f ε f 2 β (1 − α ) φ k ε f ρ f ν ft ∂φ s − C3ε f − C4ε f f ( s − 1) gδ j 3 k k φ σ c ∂x j φf EP 220 SC is the Stokes number modeled by particle response time and characteristic time scale of M AN U 218 ) =O = 1.44, &O = 1.92, O (10) = 1.2, and (O = 1.0 where the empirical coefficients are selected as 223 [Rodi, 1993; Cheng et al., 2017]. Similar to Eq. (9), the damping effect due to particle inertia and 224 buoyancy effect due to the density stratification are included in the fourth and last terms on the 225 RHS of Eq. (10). The empirical coefficient PO 226 stratification while it is automatically adjusted to PO AC C 222 227 11 is defined as PO = 0 for stable density = 1 for an unstable stratified condition. ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 228 2.2.2 Particle stress closures 229 The particle stresses due to intergranular interactions can be generated by intermittent 230 collision and enduring contact/frictional forces. The particle pressure, ! , and shear stress, . / , are modeled as consisting of a collisional component (superscript “ Q ”) and a frictional contact 232 component (superscript “ 233 ps = psc + psf , 235 τ ijs = τ ijsc + τ ijsf . (11) (12) M AN U 234 SC ”) [e.g., Hsu et al., 2004]: RI PT 231 236 The collisional component of particle pressure, ! 3 , and particle shear stress, . 3 , are modeled 238 through the granular temperature obtained from the kinetic theory of granular flow [Jenkins and 239 Savage, 1983; Ding and Gidaspow, 1990]. The granular temperature accounts for advection, 240 diffusion, shear production, and dissipation caused by inelastic collision and particleinduced 241 fluctuations [Ding and Gidaspow, 1990; Cheng et al., 2017]. Where sediment concentration is 242 high enough, intermittent particle collisions rarely occur, and the modeled granular temperature 243 decreases. In such a dense mobile sediment layer, the frictional contact component becomes the 244 dominant contribution to the particle pressure and particle shear stress. The frictional contact 245 components of particle pressure, ! , and particle shear stress, . , are modeled following 246 Johnson and Jackson [1987] and Gidaspow [1994], respectively. The threshold values are 247 specified as 248 enduring contact becomes dominant. More detailed formulation is provided in Cheng et al. 249 [2017]. AC C EP TE D 237 = 0.57 where the variable represents the threshold concentration where 12 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 250 251 3. Results 3.1 Experimental setup 253 In BARSED, a fixed, scaled down barred beach profile was constructed based on an 254 observed beach profile during the Duck94 experiment [Garcez Faria et al., 1996; Gallagher et al., 255 1998; Scott et al., 2005], with a sediment pit installed on the sandbar crest. The wave flume has 256 an overall length of 104 m, width of 3.7 m, and depth of 4.6 m. The still water depth during tests 257 was 2.448 m at the wave maker and 1.001 m at the sandbar crest. The sediment pit dimensions 258 were 3.66 × 3.66 × 0.17 m (length × width × depth), and it was filled with sediment of median M AN U SC RI PT 252 259 grain diameter, S8T = 0.17 mm (S=T = 0.08 mm and SUT = 0.27 mm) and specific gravity of = 260 2.65. An array of sensors was positioned over the sandbar crest to measure velocity and 262 sediment concentration profiles in the sheet flow and suspended load layers. The velocity profile 263 was measured with a vertical array of six acoustic Doppler velocimeters (ADVs; 100 Hz) 264 spanning the water column from 0.1 m to 1.1 m above the initial sediment bed level with a 265 vertical spacing of 0.2 m. Nearbed velocity profiles up to 0.021 m above the sediment bed at 266 0.001 m resolution were measured using acoustic Doppler profiling velocimeters (ADPVs; 100 267 Hz). Suspended sediment concentration profiles were measured in the lower half of the still 268 water column with dualarray fiber optic backscatter sensors (FOBS; 8 Hz) with a vertical 269 resolution ranging from 0.01 to 0.07 m, and nearbed sediment concentration profiles were 270 measured using conductivity concentration profilers (CCPs; 8 HZ) [Lanckriet et al., 2013] 271 yielding 272 addition, the crossshore and vertical pore pressure gradients were obtained from an array of AC C EP TE D 261 up to 0.02 m above the sediment bed with a vertical resolution of 0.001 m. In 13 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering buried pore pressure transducers (100 Hz). Free surface elevation was observed at the cross 274 shore center of the sediment pit with a pressure gauge, !T , positioned a few centimeters above 275 the sediment bed. The crossshore variation of free surface elevation was measured using 11 276 twinwire capacitance wave gauges and 6 ultrasonic wave gauges with a sampling rate of 100 277 Hz. RI PT 273 In BARSED, each trial consisted of generating 10 monochromatic waves, with ramp up 279 and ramp down phases at the start and end of each trial. Flow velocity and sediment 280 concentration data were separated into individual wave events based on zero upcrossings of 281 !T 282 S1T7H60 [Mieras et al., 2018], which is composed of data from three separate trials containing 283 29 waves in total [Mieras et al., 2019]. A monochromatic wave train with wave period (T) of 7.0 284 s and wave heights of 0.60 m was generated at the wave maker, and subsequently shoaled to 0.94 285 m at the sandbar crest [Anderson et al., 2017; Mieras et al., 2017, 2019]. For a trial V = 7.0 s, 286 roughly three waves were present within the 20 s ramp up phase. Thus, the first three waves in 287 the signal for each trial of S1T7H60 correspond to the ramp up phase were ignored in the zero 288 upcrossing analysis. Additional details about the experimental setup, wave conditions, and data 289 analysis are provided in Anderson et al. [2017] and Mieras et al. [2017, 2019]. 291 292 M AN U EP TE D . Model validation and further discussion will be conducted using observations from case AC C 290 SC 278 3.2 Numerical model A 2DV numerical model domain (Fig. 1) was created assuming the homogeneity of 293 turbulent flow statistics in the spanwise direction (y). The positive xdirection is denoted as the 294 wave propagation direction and x = 0 is defined at the crossshore center of the sediment pit. The 295 zcoordinate (vertical) is defined as positive upward and z = 0 is located at the top of initial 14 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering sediment bed level, 1.001 m below the initial still water level. The mesh was first generated with 297 uniform grids of 16 mm in width and 8 mm in height. Near the two ends of the sandbar crest, 298 nonrectangular grids were used to resolve sharp bathymetry gradients. The grids near the edges 299 of the sediment pit were refined with three layers of unstructured triangular meshes using the 300 snappyHexMesh tool (Fig. 1a) [Jackson, 2012]. As a result, the sediment pit was shortened by 301 0.55 m from each side so that only rectangular grids were used to resolve high concentration 302 sheet flow transport with a final grid size of 2 mm (width) and 1 mm (height). A total number of 303 4.6 million grid points were used. The resulting sediment pit length in the numerical model is 304 2.56 m (compared with the experimental pit length of 3.66 m), which is shown later to be 305 sufficiently long to preserve a quasiequilibrium region in the streamwise direction. M AN U SC RI PT 296 306 The numerical wave flume geometry is identical to the physical experiment, except a 307 relaxation zone of one wave length [Jacobsen et al., 2012] was added at the inlet ( = −79.26 m 308 to 309 1c). In the numerical model, a 50th order stream function was used to generate monochromatic 310 waves, consistent with the physical experiment. For the immobile concrete beach profile, a wall 311 boundary with noflux boundary condition was applied for scalar quantities. For velocities, the 312 wallnormal component was specified to be zero and a noslip boundary condition was applied to 313 the wallparallel component. Atmospheric and empty boundary conditions of OpenFOAM were 314 adopted for the top boundary and two lateral boundaries, respectively. TE D EP AC C 315 = −45.14 m) to mimic the wave maker and its active wave absorption capability (Fig. 1b – The spatial and temporal evolution of sediment transport driven by surface waves over 316 the sandbar crest are shown in Fig. 2. The spatial evolution is presented as an 317 snapshot of volumetric sediment concentration ( 318 velocity ( − W plane ) in the sediment pit at = 59 s with fluid ) vectors overlaid (Fig. 2a). The instantaneous location of immobile bed location 15 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering (defined as the elevation where  320 accumulation of sediment was observed at the upstream and downstream edges of the sediment 321 pit, respectively, due to net onshore sediment transport driven by the surface waves. However, 322 the central region of the sediment pit far enough from these edge effects, where the range of 323 −0.42 m < 324 flow velocity and sediment concentration are homogeneous in the 325 equilibrium in the direction. For instance, the index of agreements [Willmott, 1981; Willmott 326 and Wicks, 1980], [\, of the vertical profiles of waveaveraged sediment flux were greater than 327 0.999. Moreover, the orbital excursion amplitude was roughly 1 m in this case [Mieras et al., 328 2017]; hence, advection of suspended sediment from the transitions at the offshore/onshore 329 flanks unlikely impacted the central region of the sandbar crest. Thus, flow and sediment 330 transport quantities are in quasiequilibrium in the streamwise direction for this 0.77 m long 331 span, and the shortened sediment pit length in the model plays a negligible role when examining 332 model results in the middle of the sediment pit ( = 0). < 0.35 m (a span of 0.77 m) was found to yield a region where waveaveraged SC direction, i.e., quasi M AN U TE D 333  < 107P m/s) is denoted by the dashed curve. Scour and RI PT 319 The temporal evolution of up to the seventh wave at = 0 is shown in Fig. 2b. An investigation of Reynoldsaveraged numerical model results suggests that the vertical profiles of 335 waveaveraged sediment fluxes are qualitatively similar among the fifth to seventh waves 336 ([\ > 0.934) after a vertical coordinate shift (see Section 3.3.2) to account for lowered sediment 337 bed level due to net onshore sediment transport. AC C 338 EP 334 It should be pointed out that an unrealistically large TKE can develop beneath surface 339 waves using the standard kε (and other two equation) turbulence models, as shown by several 340 previous studies [Brown et al.,2016, Devolder et al., 2017; Larsen and Fuhrman, 2018]. Larsen 341 and Fuhrman [2018] showed that this problem is not restricted to the nearsurface region, and is 16 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering rather due to the unconditional instability of two equation closure models in the nearlypotential 343 flow region beneath surface waves. However, our numerical experiments suggest the over 344 predicted TKE, which grows fastest at the free surface (see Eq. 2.12 in Larsen and Fuhrman, 345 2018), does not impact the sediment bed for the present study [Kim, 2018], which focuses on the 346 analysis under the seventh waves (between two black dotted lines in Fig. 2b). A formally stable 347 turbulence model, making use of the modified eddy viscosity approach as shown by Larsen and 348 Fuhrman [2018], will be incorporated in a future extension of SedWaveFoam. SC RI PT 342 M AN U 349 3.3 Model validations 351 The measured data were obtained from three repeated trials, so that the development of 352 undertow and the effect of decreasing/increasing sediment bed level change at the sandbar crest 353 due to net sediment transport were minimized. The measured data obtained from the last ten 354 waves (fourth to 13th waves) of each trial were used to calculate the phaseaveraged (or 355 ensembleaveraged) quantities and numerical model validation is conducted with these averaged 356 measured data [Mieras et al., 2017, 2019]. EP 357 TE D 350 3.3.1 Flow characteristics 359 Fig. 3 shows the modeldata comparison of free surface elevation (η) at four selected AC C 358 360 crossshore locations, where the instantaneous measured η was averaged across the three trials. 361 In carrying out model versus measured data validation, the ramp up portion of the signal ( ≤ 30 362 s) was ignored because of different wave generation methods between the physical experiment 363 and numerical model. For the model validation, IA and normalizedrootmeansquare errors 364 (NRMSE) are used to represent the similarity of trend and the mean of squared errors with 17 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering reference to the range of measured data, respectively. The overall agreement between measured 366 and modeled η was IA = 0.995, 0.936, 0.941, 0.936 at x = 27.41 m, 1.93 m, 1.73 m, 16.37 m, 367 respectively. The NRMSEs normalized by maximum measured wave height at each location 368 were 4.8%, 8.1%, 11.2%, 10.2%. In general, a better agreement was obtained at the locations 369 seaward of the sandbar crest. However, the model was able to capture highly skewed and 370 asymmetric nearbreaking and broken waves over the sandbar. Recorded visual observation from 371 the physical experiment indicated waves broke about 1 m landward of the center of the sediment 372 pit matching present model results. Hence, the sediment transport near the center of the sediment 373 pit is driven by highly skewed and asymmetric nearbreaking waves and wave breaking 374 turbulence is unlikely to affect nearbed sediment transport in this case [Kim, 2018]. SC M AN U 375 RI PT 365 The two main components of fluid velocity (streamwise: and vertical: ) at the center of the sediment pit are shown at three selected vertical locations in Fig. 4, coinciding with 377 the elevations of three ADVs from the experimental study. Reynoldsaveraged model results for 378 the seventh wave (black curves in Fig. 4) are compared with phaseaveraged measured data (gray 379 curves in Fig. 4). The model was able to predict velocities 380 0.996 (0.978, 0.986, 0.968) and NRMSE (normalized by measured 381 5.7%, 6.4% (12.7%, 7.1%, 5.1%) at W = 0.516 m, 0.315 m, and 0.121 m, respectively. In both 382 experimental observations and model results, has a similar magnitude at different vertical 383 locations (left column) while the magnitude of is reduced by 61.2% on average approaching 384 the sediment bed (right column). AC C EP TE D 376 385 18 ( ) with IA of 0.997, 0.997, _`a or _`a ) of 5.7%, ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 3.3.2 Wave bottom boundary layer and sediment transport 387 The sediment bed level associated with each wave was slightly different due to nonzero 388 net sediment transport. Hence, a local vertical coordinate system for each wave (ensemble) was 389 introduced in Mieras et al. [2017, 2019] to ensure the vertical profiles are referenced to the same 390 local initial sediment bed level for phaseaveraging. The inflection point of 391 & RI PT 386 , i.e., ⁄ W ∗ & = 0, was identified based on fitting a curve to the sediment concentration profiles following O’Donoghue and Wright [2004a], and defining W ∗ = 0 as the elevation of the 393 inflection point at 394 results for consistency. The sediment bed level decreased from W = 2.2 mm to 3.4 mm in the 395 model results, from the fourth to the seventh wave (see Fig. 2b). SC 392 M AN U /V = 0 for each ensemble. The same approach was applied to the model at W ∗ = 30 mm above the sediment bed agrees well with The modeled time series of 396 measured data (IA = 0.998 and NRMSE = 3.8% in Fig. 5a). In the present case, the maximum 398 modeled wave bottom boundary layer (WBBL) thickness was about 30 mm (see Section 4.1); 399 hence 400 stream, modeled (measured) velocity skewness was 4 = 0.61 (0.65) and :@ = 0.38 ( 0.58 ) TE D 397 at W ∗ = 30 mm is hereafter considered as the freestream velocity, c,_`a ie c,_`a c,_fg h At the free where the quantities are defined as 4 = 402 2004] and :@ = 〈e 403 Similarly, acceleration skewness can be quantified through 1 = l c,_`a ie l c,_`a − l c,_fgh 404 [e.g., van der A et al., 2013] where l c = EP 401 〉i〈e AC C ch ch & 〉 /& − c. [e.g., Watanabe and Sato, , in which 〈 〉 represents the waveaverage operator. c/ & and : = 〈e l c h 〉i〈e l c h 〉 /& [e.g., Drake 405 and Calantoni, 2001]. At W ∗ = 30 mm, 1 = 0.73 (0.67) and : = 2.31 (2.18) were obtained 406 for model results (measured data). The numerical model was able to reproduce important higher 407 order flow statistics relevant to sediment transport. Moreover, it is expected that sediment 19 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 408 transport in this case is driven by both highly velocityskewed and accelerationskewed waves 409 (see Table 1). 410 Vertical profiles of at the center of the sediment pit at several instants are also compared (Fig. 5b – 5i). In the physical experiment, velocities in the high sediment 412 concentration sheet flow layer could not be measured due the attenuation of high frequency 413 acoustic signal from the ADPV. Velocities observed within the sheet flow layer were 414 subsequently discarded following Mieras et al. [2019]. The agreement of 415 local acceleration occurs (i.e., 416 overpredicted overshoot of 417 (NRMSE = 15.7%, Fig. 5c). At other instants, the model is able to predict 418 NRMSE = 11.3%, 12.3%, 4.7%, 11.6%, and 6.5% at /V = 0.086, 0.257, 0.657 , 0.886 , and 420 SC / profiles when high > 2 m/s & , Fig. 5a) are less satisfactory due to M AN U at /V = 0.014 (NRMSE = 46.4%, Fig. 5b) and /V = 0.043 profiles well, with 0.943, respectively (see Fig. 5d, 5e, 5g, 5h, 5i). Fig. 6 shows modeldata comparison of nearbed TKE at eight different instants. A high TE D 419 RI PT 411 pass filter with a selected cutoff frequency was applied to m 422 ensemble is defined as an individual wave, where the fourth through the 13th waves in each trial, 423 with three total trials, yielded 29 ensembles) using the Butterworth filter for the measured data, 424 in which n represents the demeaned quantity where 425 extract turbulent velocity fluctuations, m 426 currents, waves, and long waves in the wave flume. The magnitude of measured TKE is slightly 427 sensitive to the chosen cutoff frequency (Fig. 6). Thus, measured TKE was calculated with three 428 different cutoff frequencies (i.e., 0.5 Hz, 1 Hz, and 2 Hz) as AC C EP 421 o /V, W ∗ for each ensemble (an /V, W ∗ = 〈 W∗ 〉 + m /V, W ∗ , to /V, W ∗ , while excluding the influence of evolving 429 20 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering k (t / T, z ) = f 430 * u% if ' (t / T, z*)⋅ u% if ' (t / T, z*) 2 , (13) 431 in which p = 1, 2, 3 and “ q ” represents the ensembleaverage operator for the measured data. In 433 SedWaveFoam, TKE was directly computed from the RANS model (Eq. 9). Regardless of the 434 uncertainties in the choice of cutoff frequency, the qualitative agreements between measured 435 data and model results are very good. Quantitative comparisons between measured and modeled 436 TKE are made using a cutoff frequency of 1 Hz, suggested by a previous study using the same 437 large wave flume with similar bathymetry and instrumentation [Scott et al., 2005]. In general, the 438 magnitude of modeled TKE under the seventh wave agreed well with the measured data. Using 1 439 Hz as the cutoff frequency, we obtained NRMSE = 40.0% (Fig. 6c), 38.6% (Fig. 6d), 31.4% 440 (Fig. 6e) under the wave crest, and 28.6% (Fig. 6g), 59.7% (Fig. 6h), 43.3% (Fig. 6i) under wave 441 trough. Generally, the nearbed TKE is on the order of O 107 ~107& m& /s & under wave crest SC M AN U TE D 442 RI PT 432 while it is reduced to O 107 m& /s & during flow reversal (Fig. 6b and 6f). In particular, very close to the sediment bed in the sheet flow layer (W ∗ < 6 mm), model results suggest a rapid 444 increase of TKE during the acceleration phase (Fig. 6c, 6d, 6g, 6h) by almost an order of 445 magnitude larger compared with that above the sheet flow layer. AC C 446 EP 443 / Vertical profiles of normalized volumetric sediment concentration ( _`a ) are 447 compared at the same eight instants as before (Fig. 7b – 7i in linear plots and 8b – 8i in semilog 448 plots with a wider y axis). The agreements between measured and modeled 449 were good (IA = 0.992, 0.995 and NRMSE = 5.6%, 4.5% at /V = 0.086 and 0.886 , 450 respectively) under the wave crest (Fig. 7d) and trough (Fig. 7h). Discrepancies in the higher 451 concentration region during flow reversal (Fig. 7b and 7f) may be due to the fact that the CCP 21 / _`a profiles ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering / _`a > 0.03 ) used in the physical experiment to estimate sediment sensor (covering 453 concentration tends to smooth out the concentration profile at the socalled shoulder (IA = 0.990, 454 0.992 and NRMSE = 6.5%, 5.8% at /V = 0.014 and 0.443, respectively). The minimum sheet 455 flow layer thickness that can be resolved by the CCP is about 5 mm [Lanckriet et al., 2014] while 456 the model results suggest that the sheet flow layer thickness can be as small as 1 mm during 457 onshoretooffshore flow reversal (see more discussion later). Notable discrepancy is observed 458 in the very dilute region ( 459 exhibited a nearly uniform sediment concentration profile ( 460 attributed to wash load and uncertainties in calibration of sensors. Thus, the contribution of 461 sediment flux in the dilute region is excluded in the following sediment transport rate 462 comparison for both measured and modeled data. In the model results, the contribution of very 463 dilute region to sediment transport rate was less than 5.5% on average. Overall, SedWaveFoam 464 can reproduce the general shape of the volumetric sediment concentration profile (Fig. 7 – 8). SC < 0.01) in the semilog plots (Fig. 8). The measured data / _`a ≈ 0.01) which might be M AN U TE D (u ) with reference to the time series of are shown in Fig. 9. The instantaneous elevation of the top of sheet flow layer (W ∗ ) is defined at the vertical location of EP 467 _`a The temporal evolution of sheet flow layer thickness (G ), and sediment transport rate 465 466 / RI PT 452 = 0.08 [DohmenJanssen ∗ et al., 2001; Ribberink et al., 2008]. The instantaneous sediment bed location (Wvwx ) of model 469 results is defined where streamwise sediment velocity, 470  AC C 468 , is smaller than a threshold value,  < 5 × 107P m/s, representing a nearly immobile bed. The sheet flow layer thickness, G , is 471 ∗ ∗ defined as G = W ∗ − Wvwx . In the measured data, Wvwx was estimated as the elevation of the 472 intersection between a straight line extended outward from the inflection point of 473 following the slope based on a composite power law profile, and a vertical straight line through 474 _`a W∗ [Mieras et al., 2017]. Due to the aforementioned smoothing effect from the CCP, measured 22 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 475 476 477 G can be overpredicted, and requires a correction formula to obtain the true G [Lanckriet et al., 2014]. The modeled G was close to the measured G where IA = 0.876 and NRMSE = 19.1%. The maximum sheet flow layer thickness (G ,_`a ) was about 10 mm in this case. As pointed out before, velocity profiles in the sheet flow layer were not directly measured 479 during the physical experiment. However, velocity information is critical in estimating the time 480 dependent sediment transport rate, u , using the measured sediment concentration data. In the 481 sheet flow layer, 482 ∗ at Wvwx [Mieras et al., 2019]: RI PT 478 483 α z * −z *bed u (t / T , z*)n = u (t / T , z *s )n δs n s 484 485 f (14) where n represents each wave (i.e., ensemble), and I is a profile shape parameter (0 < I ≤ 1) TE D 486 M AN U SC was approximated by extrapolating the measured velocity at W ∗ down to zero [Sumer et al., 1996; Pugh and Wilson, 1999; Wang and Yu, 2007; Puleo et al., 2017], where I = 488 1.0 is a linear profile. It is important to point out that this formula assumes 489 the measured velocity from the ADPV. The model results confirm that 490 the top of sheet flow layer (W ∗ = W ∗ 491 the 492 (i.e., a linear profile) gave the smallest NRMSE and largest IA (not shown here). Hence, I = 1.0 493 is adopted to reproduce the full profile of streamwise velocity in the measured data. In addition, 494 the results of using a squarerootshaped ( I = 0.5 ) profile to approximate the streamwise 495 velocity in the sheet flow layer are also presented. EP 487 at W ∗ to be equal to and are identical at ) where IA = 1 and NRMSE = 0.1% (Fig. 9a). Comparing AC C profiles calculated by SedWaveFoam with those from Eq. (14), it was found that I = 1.0 23 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering The timedependent u was calculated by integrating the horizontal sediment flux over 496 497 the water column as: 498 z*1 ( t ) z*bed (t ) φ s (t / T , z*)u s (t / T , z*)dz * 500 (15) 501 where W= represents the vertical elevation where 502 that 503 discussed before, and contribution of 504 smaller than that of 505 compared with estimated u (measured) for both I = 0.5 and 1.0 (Fig. 9c). Measured u using = 0.01. It should be reiterated here < 0.01 were excluded for both measured and modeled u due to the wash load / y C / y C SC y C y C < 0.01 to sediment transport rate was much M AN U 506 / / RI PT q s (t / T ) = ∫ 499 ≥ 0.01 in the model results. SedWaveFoam results (modeled) are I = 1.0 agrees reasonably well with the SedWaveFoam results. However, measured u magnitude using I = 0.5 (gray dashed curve in Fig. 9c) is larger compared to the other two 508 curves, particularly under the wave crest. The IA and NRMSE of SedWaveFoam results 509 compared with measured u were 0.968 (0.919) and 8.5% (16.1%) with reference to the I fitted TE D 507 measured data using I = 1.0 ( I = 0.5 ). Some discrepancies between model results and 511 measured data may be attributed to the smoothed vertical profile of measured 512 multiplied with 513 concentrations during lowflow phases in the wave cycle (i.e., small sheet flow layer thickness) 514 (see Fig. 7 – 8). However, the smoothing effect becomes negligible for increasing sheet flow 515 layer thickness ( ≳ 6 mm), when the magnitude of the timedependent sediment transport rate is 516 EP 510 which was AC C without any correction for potentially over or underpredicted sediment largest. Measured waveaveraged sediment transport rate (net sediment transport rate), 〈u 〉, was 517 115.77 mm& /s using I = 1.0 and 148.86 mm& /s using I = 0.5 . Hence, u in the sheet flow 518 layer is sensitive to the approximation of the shape of the 24 profile in the sheet flow layer, as ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 519 520 〈u 〉 varies by roughly 30% depending on the I value. Modeled 〈u 〉 was 102.58 mm& /s, which is within 11.4% discrepancy compared with the measured data using I = 1.0. 522 4. Discussion RI PT 521 4.1 Effect of progressive wave streaming 524 Net onshore sediment transport can be enhanced under free surface waves due to the 525 effect of progressive wave streaming [Nielsen, 2006; Holmedal and Myrhaug, 2009, Kranenburg 526 et al., 2012, 2013; Fuhrman et al., 2013; Kim et al., 2018], a process not present in OWTs. 527 Following the methodology used by Kim et al. [2018], the 1DV SedFoam model is applied to 528 simulate the S1T7H60 case without a free surface to contrast the results with SedWaveFoam so 529 that free surface effects can be isolated. It should be noted here that the main differences between 530 SedWaveFoam and 1DV SedFoam are that SedWaveFoam results include the progressive wave 531 streaming effect [Nielsen, 2006; Holmedal and Myrhaug, 2009, Kranenburg et al., 2012, 2013; 532 Fuhrman et al., 2013; Kim et al., 2018] and convergingdiverging effect on a sloping bed [Sumer 533 et al., 1993; Fuhrman et al., 2013]. A simple scaling analysis following Fuhrman et al. [2013] 534 suggests that for the present wave condition and beach slope, the convergingdiverging effect 535 may be of minor importance relative to the progressive wave streaming effect. Nevertheless, it is 536 worthwhile to point out the possible effect of convergingdiverging on a sloping beach when 537 interpreting the present model results. The vertical grid size and model parameters of 1DV 538 SedFoam are identical to those used in the validated SedWaveFoam model. Flow is driven in the 539 SedFoam model by a prescribed horizontal pressure gradient ( 540 streamwise flow velocity ( 541 the WBBL) with AC C EP TE D M AN U SC 523 wa wa ) calculated using the ) of SedWaveFoam at W ∗ = 0.15 m (sufficiently far enough from =− ! ⁄ = ⁄ following the boundary layer approximation. 25 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 542 Consistent with previous analysis, SedFoam model results under the seventh wave are selected 543 for the model intercomparison. 544 at W ∗ = 0.1 m produced by the 1DV SedFoam simulation is almost The time series of identical to that of SedWaveFoam (IA > 0.999 and NRMSE = 1.4% in Fig. 10a). Thus, the 546 external forcing condition imposed to the 1DV SedFoam model is appropriate for a direct 547 comparison of sheet flow dynamics between the models. The timedependent WBBL thickness is 548 ∗ estimated as G = W ∗ − Wvwx where W represents the velocity profile overshoot, defined as the 549 vertical elevation of maximum 550 Kim et al., 2018]. The overshoot of 551 free surface waves, leading to the inability to determine W ∗ for SedWaveFoam results SC in time [Jensen et al., 1989; O’Donoghue and Wright, 2004b; is less easily discernible during the wave trough under M AN U 552 RI PT 545 occasionally. In general, the increase of G is more rapid when a free surface is included (SedWaveFoam), but maximum G values from both models are similar (Fig. 10b) with a 554 maximum WBBL thickness of about 30 mm. TE D 553 555 Both models illustrate large TKE under the wave crest ( :_`a of 0.021 m& /s& in 556 SedWaveFoam and :_`a of 0.017 m& /s & in 1DV SedFoam) compared to that under the wave trough (:_`a of 0.007 m& /s & in SedWaveFoam and :_`a of 0.006 m& /s & in 1DV SedFoam) due 558 to velocity skewness (Fig. 10f – 10g). This feature is known to cause turbulence asymmetry 559 which leads to wave shape streaming [Kranenburg et al., 2012] and an offshoredirected mean 560 current. 561 velocity, 〈 562 10e). Near the sediment bed, however, the vertical profile of 563 onshoredirected, particularly under the wave crest (Fig. 10c) owing to the onshoredirected 564 progressive wave streaming. Here, the progressive wave streaminginduced mean current is AC C EP 557 Both models show consistent offshoredirected waveaveraged streamwise fluid 〉, approaching 0.14 m/s, sufficiently away from the sediment bed (W ∗ > 0.1 m, Fig. 26 in SedWaveFoam is more ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 565 computed through the waveaveraged instantaneous velocity difference between the two models 566 (i.e., 〈 567 directed current with a peak velocity (〈 568 is inside the WBBL. Notice that the mean current of SedWaveFoam mostly remains to be 569 offshoredirected due to the stronger effect from the wave shape streaming, but it is evident that 570 the progressive wave streaming causes the magnitude of the offshoredirected mean flow to be 571 reduced within the WBBL. When a free surface is included, two different boundary layer 572 streaming mechanisms generate competing currents which induce stronger shear in flows, 573 resulting in one order of magnitude larger TKE (Fig. 10f – 10h) above the WBBL (W ∗ > 30 574 mm). The progressive wave streaminginduced mean current for nearbreaking waves is about 575 30% larger than that observed under nonbreaking waves where 〈 576 0.044 m/s in Kim et al. [2018]; although, 577 the sediment bed for both results) is smaller for BARSED ( 578 under nonbreaking waves ( 579 mechanism altering (enhancing) the streaming current. As will be discussed later, larger 580 magnitude horizontal pressure gradient (characterized by l c ) for nearbreaking waves can be 581 considered a major factor enhancing the streaming current. ~wx•`€w•‚`_ − ~wx•‚`_ 〉 ). The vertical profile of 〈 〉 xf}} _`a ) xf}} 〉 shows onshore of 0.056 m/s at W ∗ = 0.017 m (Fig. 10e) which M AN U SC RI PT 〉=〈 = …〈 −〈 TE D ƒ„~ 〉 xf}} _`a was computed as 〉 & 〉 (computed at 0.15 m above ƒ„~ = 0.31 m/s) compared to that = 0.64 m/s). The difference suggests there is an additional EP ƒ„~ AC C 582 xf}} To study sheet flow processes in detail, the vertical profiles of (top row), (middle 583 row), and streamwise sediment fluxes, , (bottom row) under the wave crest (left column), 584 wave trough (middle column) and the corresponding waveaveraged profiles (right column) are 585 shown in Fig. 11. Under the wave crest, sediment was suspended higher in the water column 586 (Fig. 11a) with larger magnitude in in the onshore direction (Fig. 11d) when a free surface 27 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 587 was included (SedWaveFoam), and the resulting waveaveraged onshore sediment flux, 〈 588 was significantly larger than for the OWTdriven (1DV SedFoam) results (Fig. 11i). On the 589 contrary, the corresponding vertical profiles of 590 trough (Fig. 11b, 11e, 11h) for both model simulations. The free surface enhances net onshore 591 flux (Fig. 11i) with the major difference occurring within the WBBL. The increase of onshore 592 directed 593 velocityskewed waves for S8T = 0.24 mm and wave velocity skewness of 0.39 (see Table 1 for 594 more information) [Kim et al., 2018], compared with identical forcing with no free surface. The 595 enhancement in net sediment transport rate was explained by a wavestirring mechanism in 596 which greater sediment concentration associated with a velocityskewed wave crest was carried 597 onshore by the progressive wave streaminginduced current. For the present nearbreaking waves 598 with both large velocity and acceleration skewness, the waveaveraged net onshore sediment 599 transport rate was increased by 346% due to the free surface effect (see Table 1), nearly 6 times 600 the effect for the nonbreaking velocityskewed condition reported by Kim et al. [2018]. The 601 more significant enhancement of onshore sediment transport for the nearbreaking wave 602 condition must be further related to additional mechanisms that serve to enhance the wave 603 stirring effect (see Section 4.2). , and were similar under the wave RI PT , 〉, EP TE D M AN U SC due to the free surface effect was previously shown to be 59% for nonbreaking AC C Further insights into sediment transport are found by separating the sediment flux into 604 605 current and waveinduced components. For the Reynoldsaveraged model results, the total 606 waveaveraged sediment flux, 〈 607 608 609 〈 † 〉〈 〉, was decomposed into the currentinduced sediment flux, 〉 , and waveinduced sediment flux, 〈 † m 〉 where /V, W ∗ and /V, W ∗ = 〈 W∗ 〉 + m /V, W ∗ = 〈 W∗ 〉 + /V, W ∗ (Fig. 12). Below W ∗ = 0, the results from SedWaveFoam and 1DV SedFoam were similar, showing onshore flux in 〈 28 〉〈 〉 and offshore ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 610 flux in 〈 † m 〉 profiles. Both models indicate that the resulting total flux 〈 〉 below W ∗ = 0 611 was onshoredirected. Above W ∗ ~ 2 mm, all fluxes (total, wave, and current) from 612 SedWaveFoam were onshoredirected, markedly different from the 1DV SedFoam flux profiles. 613 The increase in magnitude of 〈 RI PT 〉 from SedWaveFoam is attributed to the progressive wave streaming, particularly from 〈 † m 〉. In other words, a small mean current (see Fig. 11f) induces 615 a considerable net onshore sediment transport when there is substantial sediment suspension 616 under the wave crest (see Fig. 11a). This observation is consistent with the wavestirring effect 617 identified by Kim et al. [2018] for nonbreaking waves. However, the net onshore sediment flux 618 is much more enhanced for nearbreaking waves (Fig. 12a) compared to that for nonbreaking 619 waves [see Fig. 9 in Kim et al., 2018], despite similar flow intensities in terms of velocity 620 skewness (4 and :@ ; Table 1). The role of the horizontal pressure gradient associated with high M AN U SC 614 acceleration skewness (characterized by 1 and : ), a feature unique to the present near 622 breaking wave conditions from BARSED, is illustrated in the next section. TE D 621 623 4.2 Effect of horizontal pressure gradient 625 Nondimensionalized horizontal pressure gradient, i.e., Sleath parameter, , is calculated 627 628 as AC C 626 EP 624 ∂p f / ∂x S =− s . (ρ −ρf ) g (16) 629 630 The time series of S for SedWaveFoam and 1DV SedFoam model results are compared with the 631 measured data (Fig. 13b). For reference, the time series of 29 is also presented (Fig. 13a). In the ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering measured data [Anderson et al., 2017], a thirdorderaccurate finite difference formula [Hoffman 633 and Frankel, 2001; Suzuki et al., 2010] was employed to calculate the horizontal pore pressure 634 gradient (over a horizontal span of 0.08 m in the crossshore), where the vertical elevation of the 635 pressure transducers was 5 ~ 10 mm below the initial sediment bed level. For the SedWaveFoam 636 model, the horizontal pore pressure gradient was calculated at W ∗ = −7.3 mm using a central 637 difference method (over a horizontal span of 0.004 m in the crossshore). The spatial variability 638 resolved by the SedWaveFoam model is shown via two time series of 639 locations, 640 horizontal pore pressure gradient of 1DV SedFoam is − ! ⁄ 641 vertically uniform. Compared with the measured data, a notable discrepancy was observed in 642 1DV SedFoam results shortly after the flow peak (0.1 < /V < 0.2) where  643 predicted by roughly 50% in comparison with the measured data (black dashed curve versus gray 644 curve in Fig. 13b). On the other hand, the SedWaveFoam model was able to predict the negative 645 peak in 646 and NRMSE = 16.8%, black dashdotted curve in Fig. 13b). Interestingly, an underestimation of 647 the negative peak in 648 solid curve in Fig. 13b), more consistent with the 1DV SedFoam results. To summarize, the peak 649 of horizontal pore pressure gradient in the surface layer of the sediment bed under wave crest 650 observed in the measured data cannot be captured by 1DV model. More importantly, the 651 SedWaveFoam model results indicate that the horizontal pore pressure gradient was not 652 homogeneous in the streamwise direction. Within a spatial variability of only 0.04 m, the 653 SedWaveFoam model showed a significant difference regarding the 654 wave crest. It appears that under surface waves with large acceleration skewness, large spatial RI PT 632 SC at different crossshore TE D M AN U = 0 and 0.04 m (Fig. 13b). Following the boundary layer approximation, the around 0.1 < /V < 0.2 at = ⁄ and must be y C was under = 0.04 m agreeing well with measured data (IA = 0.966 = 0 for SedWaveFoam (black AC C EP around 0.1 < /V < 0.2 also occurs at 30 peak shortly after the peak ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 655 variabilities in the sheet flow layer can exist. This spatial feature cannot be captured by the 1DV 656 SedFoam model which assumes a homogeneous solution in the streamwise direction. The source 657 of the spatial variability will be illustrated more clearly using the SedWaveFoam results later. 659 Nondimensionalized bed shear stress is characterized via the Shields parameter, ‡, as [Shields, 1936] 660 663 s (17) M AN U 662 τb , ( ρ − ρ f ) gd50 SC θ =− 661 RI PT 658 where the total bed shear stress, .ˆ , is calculated as the sum of the fluid shear stress (. ) and particle shear stress ( . ) at W ∗ = 0 . The temporal evolution of ‡ , G , and u between 665 SedWaveFoam and 1DV SedFoam model results are given to further demonstrate the effect of a 666 free surface (Fig. 13c – 13e). Berni et al. [2017] found that strong horizontal pressure gradients 667 destabilize the sediment bed which may reduce the bed shear stress. SedWaveFoam model 668 results presented here are consistent with this observation. Before the flow peak (0 < /V < TE D 664 0.1), the negative horizontal pore pressure gradient (or positive S) of  670 opposite direction of the flow, stabilizing the sediment bed which increases the onshoredirected 671 bed shear stress of SedWaveFoam. On the other hand, the more rapid decrease of ‡ after the flow _`a  = 0.18 acts in the AC C EP 669 672 peak (0.1 < /V < 0.2) in the SedWaveFoam results is correlated with an increase of positive 673 horizontal pore pressure gradient (or negative S) (Fig. 13b and 13c). 674 1DV SedFoam predicts smaller G and u under the wave crest while the difference is 675 less apparent at the wave trough (Fig. 13d and 13e). Maximum G from SedWaveFoam was 676 enhanced by 41.3% compared to that of 1DV SedFoam. For the present nearbreaking waves, 31 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 678 679 680 modeled u under the wave crest from SedWaveFoam was 1234.51 mm& / , which is 96.8% greater than u_`a from 1DV SedFoam (627.33 mm& /s). Under the wave trough, the difference between SedWaveFoam and 1DV SedFoam in u is relatively minor (Fig. 13e). The waveaveraged (i.e., net) sediment transport rate predicted by SedWaveFoam (〈u 〉 = 102.58 mm& /s) RI PT 677 was 3.46 times larger than that of 1DV SedFoam (〈u 〉 = 29.63 mm& /s; see Table 1). Kim et al. 682 [2018] showed that under nonbreaking waves, the enhanced onshore sediment transport 683 particularly apparent under the wave crest with the presence of a free surface is associated with 684 the wavestirring effect combined with the progressive wave streaming. With similar flow 685 intensity and velocity skewness (Table 1), the free surface effect on enhancing waveaveraged 686 onshore sediment transport 〈u 〉 for nonbreaking waves reported by Kim et al. [2018] was only 687 60%. Cheng et al. [2017] suggested that momentary bed failure may occur under combined high 688 values of ‡ and 689 resolved by a 1DV model due to streamwise uniformity. When momentary bed failure occurs, 690 the thickness of the mobilized sediment bed layer is significantly increased, often related to 691 suddenly enhanced sediment transport via plug flow [Sleath, 1999; Foster et al., 2006]. It is 692 likely that momentary bed failure associated with large horizontal pressure gradients (i.e., large 693 acceleration skewness) is occurring under the present nearbreaking wave conditions, acting as 694 an additional mechanism to enhance net onshore sediment transport in conjunction with the 695 progressive wave streaming. It is important to point out that although there was large spatial 696 variability in 697 were minor (at 698 to those at M AN U SC 681 AC C EP TE D that further leads to instabilities within the sheet flow layer, which cannot be in the streamwise direction, the corresponding spatial variabilities of G and u = 0.04 m, NRMSEs are 3.9% and 1.6% for G and u , respectively, compared = 0). 32 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 699 The spatial variability of and fluid vorticity ( ‰ = S ⁄SW − S ⁄S ) are 700 investigated using SedWaveFoam results to shed more light on possible momentary bed failure 701 (Fig. 14). The spatial variability in 702 (Fig. 14a and 14c), three locations of large   approaching 0.2 were observed. These locations RI PT is associated with nearbed vorticity. Under the wave crest also coincide with high fluid vorticity ‰ near the sediment bed. These vorticity “hot spots” are 704 present under the wave crest with high flow acceleration (Fig. 14a and 14c), but almost disappear 705 under the wave trough (Fig. 14b and 14d). The spatial variation of (or ‰ ) shown in Fig. 14a 706 (Fig. 14b) explains why SedWaveFoam pressure gradient results at = 0 differed significantly 707 from those at 708 distributed with a local length scale of about 2 cm, coincident with the bed level change. It 709 should also be noted that the bed level change is not always associated with large fluctuations of = 0.04 m, under the wave crest (Fig. 13b), as the “hot spots” were sparsely M AN U 710 SC 703 nor ‰ under the wave trough (Fig. 14c and 14d), in which large and ‡ are essential to trigger the momentary bed failure. Overall, the intermittent spatial fluctuation of 712 wave crest is consistent with the concept of momentary bed failure. 2DV SedFoam was also 713 utilized to doublecheck the generation of nearbed instabilities. Qualitatively similar spatial 714 fluctuations of 715 dimensional model is essential to resolve the effect of momentary bed failures, which is 716 necessary to reproduce observed enhanced net onshore sediment transport. under the EP and ‰ existed in the 2DV SedFoam results (not shown here). Thus, a two AC C 717 TE D 711 To further understand why net onshore sediment transport due to the free surface effect 718 under nonbreaking waves reported by Kim et al. [2018] is much smaller than the present near 719 breaking case (BARSED), the spatial evolutions of , ‰ , and of these two cases under the 720 wave crest ( /V = 0.114 for BARSED and /V = 0.205 for nonbreaking wave) are presented in 721 Fig. 15. Although the setups and dimensionless parameters between the two cases vary (e.g., 33 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 722 wave condition, water depth, and sheet flow layer thickness), this analysis has qualitative and 723 comparative value since it was evident that momentary bed failure enhancing onshore sediment 724 transport did not occur in the case studied in Kim et al. [2018]. The present BARSED case has 725 about 2.5 times larger  726 As expected, the spatial fluctuation of 727 concentration 728 nonbreaking wave case showed much less spatial fluctuations in these quantities. than that in Kim et al. [2018], due to greater 1 and : (Table 1). RI PT _`a  and ‰ are substantial in BARSED, and hence sediment SC also shows significant variation in the streamwise direction. In contrast, the The combined effects of large horizontal pressure gradients associated with high 730 acceleration skewness and large bed shear stress likely trigger nearbed instabilities, and drive 731 more sediment suspension (Fig. 11a) and onshore directed current (see 〈 732 M AN U 729 〉 xf}} _`a in Table 1). Hence, the net onshore waveinduced sediment flux (〈 † m 〉) (Fig. 12c), and sediment transport rate (u ) are significantly increased. In other words, through numerical experiments with and 734 without the presence of a free surface and comparison with earlier model results without large 735 acceleration skewness, it was demonstrated that nonlinear interactions between acceleration 736 skewness, velocity skewness, and progressive wave streaming can significantly enhance net 737 onshore sediment transport. EP TE D 733 739 740 AC C 738 5. Conclusions A numerical investigation of sheet flow under nearbreaking surface waves was 741 conducted using a free surface resolving Eulerian twophase model, SedWaveFoam. The notable 742 advantage of SedWaveFoam is that the flow fields under progressive waves over a complex 743 bathymetry and resulting sediment transport processes can be concurrently resolved. In the 744 present study, SedWaveFoam is fully validated with measured data [Anderson et al., 2017; 34 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering Mieras et al., 2017, 2019]. For the fluid characteristics, SedWaveFoam yielded excellent 746 agreement with measured free surface elevation, streamwise and vertical velocities. For the 747 WBBL and sediment transport characteristics, the vertical profiles of streamwise velocity, TKE, 748 volumetric sediment concentration, and sheet flow layer thickness show good agreement with 749 measured data. Sediment transport rates using the I fitting method are comparable with 750 SedWaveFoam results. RI PT 745 The 1DV SedFoam simulation representing conditions without a free surface is also 752 carried out and the results are compared with SedWaveFoam model results to identify the 753 different sediment transport mechanisms driving onshore sediment transport. Consistent with the 754 sediment transport under nonbreaking waves [Kim et al., 2018], the nearbed flow velocity and 755 sediment flux are more onshoredirected by including the free surface; consistent with the effect 756 of progressive wave streaming. However, it is evident that for the nearbreaking waves, onshore 757 sediment transport is further enhanced due to a large horizontal pressure gradient. Model results 758 indicate that the combined effect of large horizontal pressure gradient and bed shear stress 759 triggers nearbed instability of the sheet flow layer where the instantaneous nearbed vortices are 760 generated enhancing sediment transport under the wave crest. The locations where nearbed 761 instabilities take place coincide with the occurrence of large horizontal pore pressure gradient in 762 the time series during the wave crest consistent with measured data. The joint effects of 763 progressive wave streaming and nearbed instability drive increased sediment suspension and 764 enhanced onshore sediment transport, which are much greater than those only with the 765 progressive wave streaming effect in nonbreaking waves [Kim et al., 2018]. The analyses 766 presented in this study were based on a single sediment size of S8T = 0.17 mm. It is expected that 767 the interplay between the free surface effect, velocity skewness, and acceleration skewness may AC C EP TE D M AN U SC 751 35 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 768 be altered for different sediment sizes. For a comprehensive understanding, a variety of sediment 769 sizes and wave conditions should be investigated. 771 772 RI PT 770 Acknowledgments This study is supported by NSF (OCE1635151; OCE1356855; OCE1356978) and Office of Naval Research (N000141812785). Numerical simulations presented in this study 774 were carried out using the Mills cluster at University of Delaware, and the SuperMic cluster at 775 Louisiana State University via XSEDE (TGOCE100015). Z. Cheng would like to thank the 776 support of postdoctoral scholarship from Woods Hole Oceanographic Institution. We are grateful 777 to the developers involved in OpenFOAM who are the foundation of the model presented in this 778 paper. We would also like to thank the two anonymous reviewers for their comments and 779 insights into the cause of fictitious TKE generation in the near potentialflow region of a wave 780 field. The source code of SedWaveFoam and the case setup to reproduce the same results is 781 publicly available via Community Surface Dynamics Modeling System (CSDMS) model 782 repository maintained by GitHub: https://github.com/sedwavefoam/sedwavefoam (source code) 783 and https://github.com/sedwavefoam/BARSED (case setup). BARSED data used in this 784 manuscript were obtained through DesignSafeCI (https://doi.org/10.17603/DS2768V). AC C EP TE D M AN U SC 773 36 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering 785 References 786 Aagaard, T., and M. G. Hughes (2010). Breaker turbulence and sediment suspension in the surf 788 789 790 zone, Mar. Geol., 271, 250–259, doi:doi.org/10.1016/j.margeo.2010.02.019. Aagaard, T., K. P. Black, and B. Greenwood (2002). 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Eng., 76, 26–42, https://doi.org/10.1016/j.coastaleng.2013.01.007. 977 SC 976 Voulgaris, G., and M. B. Collins (2000) Sediment resuspension on beaches: Response to breaking waves, Mar. Geol., 67, 167–197. Wang Y.–H., and G.–H. Yu (2007). Velocity and concentration profiles of particle movement in M AN U 975 978 sheet flows, Advances in Water Resources, 30(5), 1355–1359, 979 doi:doi.org/10.1016/j.advwatres.2006.11.012. 980 Watanabe, A., and S. Sato (2004). A sheetflow transport rate formula rate formula for 981 asymmetric forwardleaning waves and currents, in Proc. 29th Conf. Coast. Eng., World 982 Scientific, 1703–1714, https://doi.org/10.1142/9789812701916_0136. 984 985 Willmott, C. J. (1981), On the validation of models, Physical Geography, 2, 184–194, TE D 983 doi:10.1080/02723646.1981.10642213. Willmott, C. J., and D. E. Wicks (1980), An empirical method for the spatial interpolation of monthly precipitation within California, Physical Geography, 1, 59–73, 987 doi:10.1080/02723646.1980.10642189. 988 EP 986 Yoon, H. D., and D. T. Cox (2010). Largescale laboratory observations of wave breaking turbulence over an evolving beach, J. Geophys. Res., 115, C10007, 990 doi:10.1029/2009JC005748. AC C 989 43 ACCEPTED MANUSCRIPT Confidential manuscript submitted to Coastal Engineering Table 1. Key sediment transport quantities of present study compared with those under nonbreaking waves. Sheet flow under nearbreaking waves (Present study) Sheet flow under nonbreaking waves [Kim et al., 2018] S8T 0.17 mm 0.24 mm Š at the sediment pit 0.94 m V at the sediment pit 7.0 s ℎ at the sediment pit 1.001 m 4 of SedWaveFoam 0.61 :@ of SedWaveFoam 0.38 1 of SedWaveFoam : of SedWaveFoam xf}} 〉_`a ƒ„~ ‡_`a of SedWaveFoam (SedFoam) at the center of sediment pit _`a  G of SedWaveFoam (SedFoam) at the center of sediment pit ,_`a EP  of SedWaveFoam (SedFoam) AC C 〈u 〉 of SedWaveFoam (SedFoam) 993 1.55 m 6.5 s SC 3.5 m 0.62 0.39 0.73 0.49 2.31 0.07 5.6 cm/s 4.4 cm/s 0.31 m/s 0.64 m/s 3.11 (2.45) 1.58 (1.41) 0.18 (0.19) 0.07 (0.08) 10.01 mm (7.00 mm) 6.25 mm (5.72 mm) 102.58 mm& /s (29.63 mm& /s) 80.27 mm& /s (50.36 mm& /s) TE D 〈 RI PT ID M AN U 991 992 44 ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 994 995 Figure 1. The numerical wave flume with (a) mesh, (b) view of the entire flume, and (c) zoomed in view near the sandbar crest at = 59 s. Different colors in (b) and (c) represent air (white), 997 water (blue), and sediment (yellow to blue represents volumetric concentration, see color bar) 998 phases. For visibility, the mesh in (a) is downsampled by 35 times in each direction and vertical 999 scale is stretched by seven times. The vertical gray dashed line at = −45.14 m in (b) EP represents the exact boundary of the inlet relaxation zone ( < −45.14 m). AC C 1000 TE D 996 45 ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1001 over the entire sediment pit at = 59 Figure 2. The snapshots of (a) sediment concentration 1003 s where vectors represent fluid velocity 1004 center of the sediment pit ( = 0) where 1005 seventh wave. The black dashed curves in (a) and (b) represent the immobile bed location. TE D 1002 . Panel (b) shows temporal evolution of at the AC C EP between two black dotted vertical lines is under 46 ACCEPTED MANUSCRIPT TE D M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering EP 1006 1007 Figure 3. (a) A schematic of wave gauge locations in the flume denoted by dashed vertical lines 1009 and the free surface elevation for measured data averaged over three trials (thick gray curves) 1010 and model results (thin black curves) at (b) 1011 and (e) AC C 1008 = 16.37 m, as indicated in (a). = −27.41 m, (c) 47 = −1.93 m, (d) = 1.73 m, ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1015 and (b,d,f) time series for measured data (gray curves, phase averaged; gray envelopes, ±1 standard deviation) and model results (black curves) at = 0 and three vertical elevations at (a,b) W = 0.516 m, (c,d) W = 0.315 m, and (e,f) W = 0.121 m. EP 1014 Figure 4. The (a,c,e) AC C 1013 TE D 1012 48 ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering TE D 1016 1017 Figure 5. (a) Time series of measured 1018 modeled (black dashdotted curve) at c (black solid curves), and = 0. (b) ⎼ (i) are vertical profiles of /V = 0.014, (c) /V = 0.043, (d) /V = 0.086, (e) /V = 0.257, (f) /V = 0.443, (g) at (b) /V = 0.657, (h) /V = 0.886, (i) /V = 0.943, as marked in (a) using vertical dashed lines. EP 1020 (gray curves), modeled AC C 1019 c⁄ c 49 ACCEPTED MANUSCRIPT 1021 TE D M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering c Figure 6. (a) Time series of modeled 1023 cutoff frequency of 0.5 Hz; red dashed curves, cutoff frequency of 1 Hz; green dashdotted 1026 /V = 0.014, (c) /V = 0.043, (d) /V = 0.086, (e) /V = 0.257, (f) /V = 0.443, (g) EP 1025 curves, cutoff frequency of 2 Hz) and modeled (black curves) vertical profiles of : at (b) /V = 0.657, (h) /V = 0.886, (i) /V = 0.943, as marked in (a) using vertical dashed lines. AC C 1024 at = 0. (b) ⎼ (i) are measured (blue solid curves, 1022 50 ACCEPTED MANUSCRIPT TE D M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1027 c 1028 Figure 7. (a) Time series of modeled 1029 modeled (black curves) vertical profiles of / y C at (b) /V = 0.014, (c) /V = 0.043, (d) /V = 0.086, (e) /V = 0.257, (f) /V = 0.443, (g) /V = 0.657, (h) /V = 0.886, (i) /V = 0.943 on a linear scale. EP 1031 = 0. (b) ⎼ (i) are measured (gray curves) and AC C 1030 at 51 ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering c 1033 Figure 8. (a) Time series of modeled 1034 modeled (black curves) vertical profiles of / y C at (b) /V = 0.014, (c) /V = 0.043, (d) /V = 0.086, (e) /V = 0.257, (f) /V = 0.443, (g) /V = 0.657, (h) /V = 0.886, (i) /V = 0.943 on a semilog scale. EP 1036 at AC C 1035 = 0. (b) ⎼ (i) are measured (gray curves) and TE D 1032 52 ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1038 TE D 1037 Figure 9. Time series of (a) modeled (solid curve) and (asterisks) at W ∗ = W and = 1039 0. (b) G of measured data (gray curve) and model results (black curve), and (c) u of measured 1040 data (gray solid curve, using 1041 model results (black solid curve). AC C EP with I = 1.0; gray dashed curve, using 53 with I = 0.5) and ACCEPTED MANUSCRIPT TE D M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering EP 1042 Figure 10. Model comparisons of fluid phase characteristics (SedWaveFoam: solid curves; 1DV 1044 SedFoam: dashed curves). (a) Time series of 1045 thickness. (c) and (f) are vertical profiles of AC C 1043 at W ∗ = 0.1 m and (b) wave boundary layer and : under the wave crest ( /V = 0.086), and 1046 (d) and (g) under the wave trough ( /V = 0.886). (e) and (h) are waveaveraged vertical profiles 1047 of and : , respectively. The dashdotted curve in (e) represents 〈 54 xf}} 〉. ACCEPTED MANUSCRIPT TE D M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1048 Figure 11. Model comparisons of sediment phase characteristics (SedWaveFoam: solid curves; 1050 1DV SedFoam: dashed curves). (a), (d), and (g) are vertical profiles of EP 1049 , , and under 1051 the wave crest ( /V = 0.086), and (b), (e), and (h) under the wave trough ( /V = 0.886). (c), (f), 1052 and (i) are waveaveraged vertical profiles of curve in (f) represent 〈 xf}} 〉. AC C 1053 , 55 , and , respectively. The dashdotted ACCEPTED MANUSCRIPT Figure 12. Contributions to (a) 〈 〉 from (b) 〈 1056 (solid curves) and 1DV SedFoam (dashed curves). 〉〈 〉 and (c) 〈 † m 〉 of SedWaveFoam AC C EP TE D M AN U 1055 SC 1054 RI PT Confidential manuscript submitted to Coastal Engineering 56 ACCEPTED MANUSCRIPT EP 1057 TE D M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1058 Figure 13. Time series of (a) modeled (SedWaveFoam at 1059 SedFoam: black dashed curves) at W ∗ = 0.10 m, (b) measured (gray curve, phaseaveraged; gray envelope, ±1 standard deviation) and modeled AC C 1060 = 0: black solid curves; 1DV at W ∗ = −7.3 mm (black solid curve), (c) 1061 modeled ‡ , (d) modeled G , and (e) modeled u . The black dashdotted curve in panel (b) 1062 represents S from SedWaveFoam at = 0.04 m and W ∗ = −7.3 mm. 57 ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering 1063 and (c – d) ‰ , under (a, c) the wave crest ( /V = 0.114) and (b, d) the wave trough ( /V = 0.886). The black dashed and black dashdotted TE D 1066 − W ∗ snapshots of (a – b) ∗ curves represent W ∗ and Wvwx , and /V values are with reference to EP 1065 Figure 14. The AC C 1064 58 = 0. ACCEPTED MANUSCRIPT M AN U SC RI PT Confidential manuscript submitted to Coastal Engineering TE D 1067 1068 Figure 15. Comparisons between the present nearbreaking wave case from BARSED (solid 1069 curves) and a nonbreaking wave case in Kim et al. [2018] (dashed curves) (see Table 1). The 1070 spatial evolution of (a) at W ∗ = −1 mm EP under the wave crest ( /V = 0.114 for BARSED, and /V = 0.205 for nonbreaking wave). AC C 1071 at W ∗ = −7.3 mm, (b) ‰ at W ∗ = −1 mm, and (c) 59 ACCEPTED MANUSCRIPT Highlights: 1. A free surface resolving Eulerian twophase flow model is validated for sheet flow driven by nearbreaking waves on a sandbar. velocity and acceleration skewed waves. RI PT 2. Onshoredirected sediment flux is enhanced due to progressive wave streaming effect for both 3. The enhancement of onshore transport is found to be more significant for accelerationskewed AC C EP TE D M AN U SC waves due to momentary bed failure.