The authors have carried out a numerical study on the dependence of the apparent bed roughness k w /k d on four dimensionless parameters (k d /h,U fc /ub ,A/k d ,f) using a one-dimensional k-l turbulence closure model. It was found that k w /k d was strongly dependent on U fc /ub , A/k d, and f but weakly on k d /h. A fitting function, Eq. ~23! for k w /k d , was then suggested based on their numerical results and was used in the three-dimensional Coastal and Marine Engineering Research Institute ~CAMERI! flow model to calculate the current velocities in water depths of up to 8 m. The mean current velocities calculated by the flow model with Eq. ~23! were shown to be always much smaller than those without Eq. ~23 !~ see Figs. 13 and 14! especially outside the surf zone. The combination of Eq. ~23! with the CAMERI flow model is of practical importance in eliminating the unnecessary computing time in coastal flow simulations. However, the authors did not make a direct comparison of Eq. ~23! with the experimental data to test the goodness of Eq. ~23!. In this discussion, the original expression Eq. ~21! is used to compare directly with the available experimental data to show how well it performs. The effects of the physical bed roughness k d and the current friction velocity U fc on k w /k d are also discussed. It is shown in the author’s Figs. 5 ~a! and 6~a! that k w /k d decreases with the angle f between the direction of wave propagation and current. However, this simulated result is not supported by the available experimental data. The dependence of k w /k d on f was experimentally studied over movable sandy beds by Bijker ~1967 !~ f575 and 90°, regular waves!, Kaaij and Nieuwjaar ~1987 !~ f50 and 180°, irregular waves!, Kampen and Nap ~1988! ~f50 and 180°, irregular waves!, and Havinga ~1992 !~ f560, 90, 120, and 180°, irregular waves!. It is shown here in Fig. 1 that k w /k d does not decrease with f as suggested in the author’s Figs. 5~a! and 6~a!. In contrast, k w /k d tends to increase with f at f<90° and reaches its maximum at f590°. It was also concluded by You ~1996a! that the effect of f on k w /k d was not important and could be omitted. It is shown in the author’s Fig. 11 that the fitting function Eq. ~21! agrees excellently with Sleath’s ~1991! model at f50° and satisfactorily with Nielsen’s ~1992! model at f50‐90°. However, a direct comparison of Eq. ~21! with the experimental data on k w /k d was not made by the authors. In Fig. 2 here, Eq. ~21! is directly compared with the experimental data of Kaaij and Nieuwjaar ~1987! and Kampen and Nat ~1988!. It can be seen that the simple models of Sleath ~1991! and Nielsen ~1992!, which omit the effect of f on k w /k d , generally agree better with the data than the complicated formula Eq. ~21!. The experimental data of Bijker ~1967! are also used to directly compare with Eq. ~21! and the simple models of Sleath ~1991! and Nielsen ~1992! in Fig. 3. It can be seen that the simple models again agree better with the experimental data than Eq. ~21!. Some of the k w /k d values calculated from Eq. ~21! are shown less than 1.0 in Fig. 3, but the apparent bed roughness k w should be always larger than or at least equal to the physical bed roughness k d . The physical bed roughness k d was estimated to be k d 580d50 inside the surf zone and k d52.5d50 outside the surf zone. You ~1996b! studied the movable bed roughness under combined wave-current flow and concluded that the physical bed roughness over a movable sandy bed was highly affected by both the waves and currents, and not a constant. It is shown by Nielsen ~1992, Fig. 3.6.4, p. 152! that k d ranges from 100d50 to 1,000d50 for rippled beds and is of the order of 100d50 under oscillatory sheet Fig. 1. Variation of k w /k d with f measured over movable sandy beds by Bijker ~1967!, Kaaij and Nieuwjaar ~1987!, Kampen and Nap ~1988!, and Havinga ~1992!.
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Nov 2, 2010
Satya P Ojha + 1
