the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Wave-driven amplification of surf-zone bottom stress on rough seabeds
Abstract. The present paper proposes a unified view of the wave-driven amplification of the wave-averaged bottom shear stress in rough seabed contexts, covering both co- and opposing wave/current cases. The analysis is first based on a series of field observations performed over the Flysch rocky shore platform of Socoa. The momentum balance is examined locally, separating the net effect of the waves on the depth- and wave-averaged momentum budget, based on velocity and pressure measurements. The present observations confirm that, in the presence of a well-developed seabed roughness, the bed shear stress is an important component of the momentum balance. The results highlight two distinct regimes depending on the breaking activity due to the intricate composition between waves and mean currents in the wave averaged shear stress. In moderately developed undertow conditions, the bottom stress brings a negative contribution to the wave momentum balance, and acts to lower the mean water level, while under saturated breaking conditions the bed friction acts to increase the wave setup. A novel empirical parameterization of the mean bottom stress under combined waves and current is proposed. The in-situ findings are complemented by a series of wave-resolving simulations on idealized closed and open beaches, confirming the complex effect of waves on the time-averaged water circulation.
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RC1: 'Comment on egusphere-2025-2285', Anonymous Referee #1, 07 Jul 2025
The results look fine and the presentation of the results is mostly good. Nevertheless, I have some questions about the analysis. Although the answers may be simple, I think it's important to include them in the paper before I can be certain that the paper is good for publication. Please see my questions and suggestions in the Supplement.
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RC2: 'Comment on egusphere-2025-2285', Dano Roelvink, 04 Aug 2025
This is an interesting paper that describes the effect of bed friction on the cross-shore momentum balance, under combined current and wave conditions, and over a very rough rocky beach. The case is interesting because in the presence of the very high roughness, the bed friction term plays a much more prominent role in the momentum balance than for a sandy beach, and the contribution of bed friction can be extracted as the residual of other, mostly measured, terms. An empirical relationship is found for the total mean shear stress divided by the mean current shear stress, as a function of the ratio between the standard deviation of the velocity and the mean current velocity. A similar relationship is found based on some tests with the wave-resolving SWASH model. The authors suggest this relationship can be built into circulation models.
The paper is well written generally and the data seem to be of high quality and useful for any further analysis or validation of models. However, I do have a few issues.
1. In the introduction, the authors refer to some, but only ery limited, research on coral reefs, which have similarly high roughness; e.g. in van Dongeren et al., 2013, where the roughness, with similar values, was found to dominate the energy balance. But similarly, much work has been done on the effects of vegetation, which has similar effects as high roughness; van Rooijen et al (2013) for instance elucidate the mechanism through which vegetation can lead to lowering of the setup, namely through streaming and skewness of the waves, which leads to an onshore force on the vegetation (and similarly on the rocky bottom in this case). In the discussion of the resulting empirical relationship I miss this kind of analysis
2. The authors refer to Feddersen et al (2000) for the mean longshore shear stress due to current and waves, but only very briefly. The cited work contains an in-depth analysis of possible approximations of the resulting mean shear stress, and based on their data select and fit one. I can see that the cross-shore mean shear stress is more complicated because of the effects of skewness but one could at least try better to explain the relationships that are found.
3. To support the claim that the relationship(s) for the cross-shore bed shear stress can be used in circulation models, we would have to know how in a general 2DH setting the cross-shore and longshore shear stresses should be computed, somehow combining these relationships with Feddersen's model (?)
4. Perhaps the parametric relationships by Soulsby et al could be useful in this context, as they give relationships for taum/(tauc+tauw) as a function of tauc/(tauc+tauw), where taum is the mean shear stress, tauc the current-related and tauw the wave-related shear stress. The parametric relations are fitted to various wave-current interaction models, for arbitrary magnitudes and angles between current and waves. But maybe the authors have a better idea how to approach my point 3.
Minor comments:
190 depend -> depending
277 For Chezy, drag coefficient does not depend on depth (Cd=g/C^2)
Ap Van Dongeren, Ryan Lowe, Andrew Pomeroy, Duong Minh Trang, Dano Roelvink, Graham Symonds, Roshanka Ranasinghe,
Numerical modeling of low-frequency wave dynamics over a fringing coral reef,
Coastal Engineering, Volume 73, 2013, Pages 178-190, ISSN 0378-3839, https://doi.org/10.1016/j.coastaleng.2012.11.004.van Rooijen, A. A., R. T. McCall, J. S. M. van Thiel de Vries, A. R. van Dongeren, A. J. H. M. Reniers, and J. A. Roelvink (2016), Modeling the effect of wave-vegetation interaction on wave setup, J. Geophys. Res. Oceans, 121, 4341–4359, doi:10.1002/2015JC011392.
Citation: https://doi.org/10.5194/egusphere-2025-2285-RC2
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