I thank Drs. You and Yin for their interest in my paper and appreciate the opportunity to clarify the issues mentioned by them. Following the order of their comments:
[1] It is not correct that the critical orbital velocity U w can be expressed as a simple function of the wave period T, by examining my Eqs. ( 13), ( 14) and (15). Eq. (13) shows that s w must first be calculated from h ws gDq c (h ws being the critical oscillatory Shields parameter, g the gravity acceleration, D the grain diameter and q c the submerged particle density), after which U w can be determined from Eq. ( 14), being equal to (2s w /qC w ) 0.5 , where q is the fluid density. The unknown wave friction factor C w in Eq. ( 14) can be derived from Eq. ( 15) (Swart, 1974), where C w = 0.00251 exp[5.21(U w T/4pD) À 0.19 ]. However, I pointed out in my paper that, as U w is not yet known, this leads to an impasse unless U w is determined from pd o /T, which requires the threshold wave orbital diameter d o in any case. Similarly, Eq. ( 40) of You and Yin needs d o to determine C w . Furthermore, their Eq. ( 41) includes h ws as calculated using my Eq. ( 12) (Soulsby and Whitehouse, 1997). To derive U w from h ws one has to use their Eq. ( 40) or go through the same steps outlined above, leading to the same impasse. I also demonstrated in Table 1 of my paper