the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The effect of strong nonlinearity on wave-induced vertical mixing
Maciej Paprota
Wojciech Sulisz
Abstract. A semi-analytical solution to advection-diffusion equation is coupled with a pseudo-spectral approach to nonlinear wavemaker model to investigate the effect of strong nonlinearity on wave-induced mixing. The comparisons with weakly-nonlinear model predictions reveal that in the case of waves of higher steepness, enhanced mixing affects subsurface layer of the water column. Including higher-order terms into free-surface boundary conditions of the wavemaker problem secures reliable estimation of the time-mean velocity field. The corrected wave-induced mass-transport velocity leads to improved estimates of subsurface mixing intensity and ocean surface temperature.
Maciej Paprota and Wojciech Sulisz
Status: final response (author comments only)
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RC1: 'Comment on esd-2022-27', Anonymous Referee #1, 18 Dec 2022
This article addresses the interesting question of the effect of wave-induced currents on mixing. The article could eventually be published, but some issues should be addressed in a major revision.
Regarding the wave generation:
It is not clear why the authors are using wavemaker theory here. In a numerical model, more elegant methods are available to intruduce waves.
While "monochromatic wavemaker motion" gives a clear number of cases to be examined, a more realistic scenario would be to consider a wave spectrumAbout the particle tracking:
The authors state that "the improvements to the method of evaluation of mass transport velocity based on the Lagrangian
particle tracking (Paprota and Sulisz, 2018) are introduced" (line 168-169). It is not quite clear what they mean by this.
Please be more specific about the improvements.
It is also not clear why we need Lagrangian particle tracking siden for example eq. (29) only uses the Eulerian velocities.About the mixing:
What is the relative size of the mixing efficiencies kappa(m) and kappa(v) ?
The authors state the the dimensionaless parameter alpha has been measured .....
Can you be more specific?In the abstract, the authors state that this work may lead "to improved estimates of subsurface mixing intensity and ocean surface temperature."
Do the authors mean in the nearshor ocean?
Note: in the caption of Table 1, the authors state that they "wave-induced vertical mixing processes in offshore conditions."
However, the parameters given in this table appear to be mostly relevant for surfzone dynamics.Two questions: 1. Does this study apply to nearshore or offshore or both? Please address this issue.
2. There could be other effects of equal or greater importance on mixing (either shallow or deep water). Please address this issue.
The arrows in Figure 2, 3 and 4 are not extremely informative. Please add more explanations of what can be seen
and learned from these figures.
In section 3.4, the authors mention "laboratory experiments" and "wave flume" many times, giving the
impression this study was conducted in a laboratory. Together with the introduction (for example third paragraph)
this leads to confusing the reader, and deflects the focus from the numerical work. Please be very clear what this
article covers, and what it does not cover, both in introduction and in discusssion.
For example, line 46: "First, the problem of the generation of waves in a laboratory flume is formulated and solved"
This is misleading.Citation: https://doi.org/10.5194/esd-2022-27-RC1 -
RC2: 'Comment on esd-2022-27', Anonymous Referee #2, 24 Mar 2023
This work discusses the the effect of higher order nonlinear terms on wave-induced mixing. I suggest acceptance subject to some significant revisions as outlined below. I have three main concens:
1. Nonlinear vs weakly nonlinear: Is this problem truly nonlinear? It seems to me that a major feature of nonlinear waves, namely wave breaking, could not be captured in this model. I suspect this case would correspond to where the expansions for phi ceased to converge. While wave-breaking is not relevant here, I feel that the requirement of convergence means the solution given is just a higher order weakly nonlinear model (as stated) and as such, the use of the term 'strong nonlinearity' in the title is misleading. Can you discuss this point and convince the reader one way or another whether this methods fully captures nonlinearity.
2. Problem setup and oceanographic relevance: The problem is pitched as being of relevance to oceanographers though the setup modelled is a labatory one. While there are results which may be relevant to the ocean, these are mixed with results which are not. For example, the flow around the wavemaker paddle is unlikely to be of interest to anyone who isn't an experimentalist. It feels as if the authors plan to compare with experiments at a later date. I would suggest reframing the paper as an engineering problem with oceanographic relevance rather than the other way around. Results could be discussed in terms of the problem studied and a new section could be included which transfers the relvant results to an oceanographic context.
3. Discussion of new material: this work is building on previous studies by the same authors and it is not entirely clear what is new. In some places old results are repeated and in others technical details are skipped and it is not immediately clear if they're covered elsewhere. I think the authors should clarify their new contributions and give a clearer exposition of their previous work, either leaning entirely on another reference or repeating enough (clearly labelled) content that the paper stand alone.
I have made various comments on the attached PDF document.
Maciej Paprota and Wojciech Sulisz
Maciej Paprota and Wojciech Sulisz
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