Sediment flux based model of instantaneous sediment transport due to pure velocity-skewed oscillatory sheet flow with boundary layer stream

Analytical Model for Graded Sediment Transport in Velocity‐ and Acceleration‐Skewed Oscillatory Sheet Flow

“…The comparison between the measured and predicted < U B > for FVS and CVS (i.e., FA5010 and CA5010 in O’Donoghue & Wright, 2004b) is not shown because that was done in Chen, Wang, et al. (2018) (see detail in figure 8 of Chen, Wang, et al., 2018). Under velocity‐skewed oscillatory flow condition, < U B > is positive at the bottom (−5.3 mm ≤ z < −4.2 mm for FVS, −4.7 mm ≤ z < −2.3 mm for M1VS, −4.0 mm ≤ z < 0 mm for M2VS, −3.5 mm ≤ z < 1.7 mm for M3VS, −3.2 mm ≤ z < 2.5 mm for CVS) due to the mobile bed effect (Ruessink et al., 2011) and is negative away from the bed ( z ≥ −4.2 mm for FVS, z ≥ −2.3 mm for M1VS, z ≥ 0 mm for M2VS, z ≥ 1.7 mm for M3VS, and z ≥ 2.5 mm for CVS) due to the asymmetry of δ B (turbulence) (Chen, Wang, et al., 2018; Ruessink et al., 2011).…”

“…(2018) (see detail in figure 8 of Chen, Wang, et al., 2018). Under velocity‐skewed oscillatory flow condition, < U B > is positive at the bottom (−5.3 mm ≤ z < −4.2 mm for FVS, −4.7 mm ≤ z < −2.3 mm for M1VS, −4.0 mm ≤ z < 0 mm for M2VS, −3.5 mm ≤ z < 1.7 mm for M3VS, −3.2 mm ≤ z < 2.5 mm for CVS) due to the mobile bed effect (Ruessink et al., 2011) and is negative away from the bed ( z ≥ −4.2 mm for FVS, z ≥ −2.3 mm for M1VS, z ≥ 0 mm for M2VS, z ≥ 1.7 mm for M3VS, and z ≥ 2.5 mm for CVS) due to the asymmetry of δ B (turbulence) (Chen, Wang, et al., 2018; Ruessink et al., 2011). The mobile bed effect means the lowest level mobilized by a strong wave crest is not mobilized at the wave trough with weak flow strength (Figure 4) (Ruessink et al., 2011).…”

“…The size‐selective entrainment effects are considered in the calculation of C i . C i is approximated by an ideal exponential function considering mass conservation (Chen, Wang, et al., 2018), that is, $$${C}_{i}(z,t)=\left\{\begin{array}{l}{C}_{m}\,\mathrm{exp}\left[-\left(1+\frac{z}{{{\Delta }}_{i}}\right)\right]\quad z\ge -{{\Delta }}_{i}\hfill \\ {C}_{m}\qquad \qquad\qquad \quad z< -{{\Delta }}_{i}\hfill \end{array}\right.,$$$ …”

“…(2013). Considering asymmetric boundary layer development, U fs and T are divided into four quarters by flow peaks and reversals to calculate f , A , and k N in the acceleration, deceleration, crest, and trough stages (Chen, Wang, et al., 2018). To save computation, the A and f are first calculated at flow peaks and reversals, and then linearly interpolated between adjacent flow peaks and reversals.…”

“…Recently, Chen, Wang, et al. (2018), Chen, Li, & Wang (2018), Chen et al. (2020) established an approximation of uniform sediment for velocity and sediment concentration profiles in velocity‐ and acceleration‐skewed oscillatory sheet flow.…”