the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Jun 2025
Analytical approaches for wave energy dissipation induced by wave-generated turbulence and random wave-breaking
Abstract. This paper is dedicated to investigate the dissipation effects of wave-generated turbulence reacting on ocean waves and to estimate the energy loss due to wave-breaking theoretically. An analytical dissipation source function induced by wave-generated turbulence in the water was proposed through the equilibrium solutions of a high-deterministic second-order turbulence closure model between the wave shear instability generations and the turbulent kinetic energy (TKE) dissipations. And an improved postbreaking spectrum expression, based on the breaking wave statistical method, was presented to depict more explicitly the intermittent wave-breaking events. Their verifications with laboratory observations or comprehensive measurements were provided, and applications on simple duration-limited growth and decay experiments were implemented. Numerical results indicate that the wave energy dissipation induced only by random wave-breaking is inadequate, sum of its contribution and that induced by wave-generated turbulence play critical roles of wave energy loss. Evaluations for more complex situations will be addressed in the future series of papers.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-2671', Anonymous Referee #1, 29 Jul 2025
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AC1: 'Reply on RC1', Meng Sun, 17 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2671/egusphere-2025-2671-AC1-supplement.pdf
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AC1: 'Reply on RC1', Meng Sun, 17 Sep 2025
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RC2: 'Comment on egusphere-2025-2671', Anonymous Referee #2, 15 Aug 2025
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AC2: 'Reply on RC2', Meng Sun, 17 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2671/egusphere-2025-2671-AC2-supplement.pdf
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AC2: 'Reply on RC2', Meng Sun, 17 Sep 2025
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-2671', Anonymous Referee #1, 29 Jul 2025
Review of "Analytical approaches for wave energy dissipation induced by wave generated turbulence and random wave-breaking” by Yang et al., manuscript egusphere-2025-2671 (my first review of this manuscript).
The authors present an interesting and detail assessment of wave energy dissipation in wind wave models. The paper is easily understandable but would benefit from editing by native English speakers.
The authors provide an extensive review of previous literature in the introduction. I applaud the authors for the completeness of the review, even though that resulted in a rather long introduction. The discussion of the linkage between oceanic turbulence and wind wave dissipation starts at line 62 with the references to Polnikov’s work and takes us through subsequent theoretical and practical understanding of these processes with many more references. The authors observe the lack of theoretical / mathematical foundation for the existing models and set forth to provide a more solid mathematical background for the link between ocean turbulence, random wave breaking and wave energy dissipation.
The next section deals with theoretical / mathematical derivations. Section 2.1 addresses the linkage between wave-generated turbulence and wave energy dissipation, culminating in Equation (15) for wave energy dissipation associated with oceanic wave-generated turbulence. The authors then compare their dissipation with wave growth formulations, where they appear to imply without saying as much that either the two source terms need to be in close balance, and/or that the balance between the two is what governs overall growth rates. It does not address the uncertainty in both terms. The old Large and Pond assessment that the uncertainty in wave growth rates from observations have an uncertainty of up to an order of magnitude, in my opinion, still holds. The comparison between dissipation rates (e.g., Fig. 3) is fairly convincing in that the bulk rates are similar as one would expect from the fact that the derivation assumes a close linkage. What is missing here or later in the paper is how (15) compares to previous formulations, and why / how it is better. Note that if it is the same, the more rigorous derivation might still fully justify publication.
Section 2.2 then addresses the second dissipation process associated with wave breaking (I assume mostly at the crest of at the dominant waves), culminating in a fairly traditional source term formulation (20) with a new dissipation coefficient (26). On line 355 Eq. (26) is introduced as “Hence we propose an improved attenuation coefficient expressed as follows”. As with the expression for the first mechanism, there is no direct comparison to previous formulations. Whereas this may be a new formulation, there is no proof presented why this is “improved”, unless one accepts that a more rigorous derivation can be considered as improved for a wave model that overall is still highly empirical. Moreover, I do not find the comparisons with observations in Figures 5 and 6 overly convincing, mostly due to the signal to noise ratio in the data.
What interests me most as a practical wave modeler, is if the new formulations show new scaling behavior compared to previously suggested models, and if they introduce new functional dependencies within the processes described here.
In Section 3 the authors apply their new sources terms in a numerical model and provide results of model integration in spatially homogeneous conditions (duration-limited growth), providing comparisons with a physics set-up of the WAM Cycle 4 model (i.e., Janssen 1994). I find this the weakest part of the manuscript for the following reasons.
- Unlike for fetch-limited growth, there are no good observations for duration-limited growth. Hence, there are no objective data to compare the model results to, and the authors (by necessity) compare their model to another model (effectively the original WAM Cycle 4).
- With using a free scaling parameter as a tuning parameter with a valid range of an order of magnitude, and with formulations of source terms that are not that different from previous versions, the software engineer in me is not surprised that it is possible to tune the models to get similar results.
- Moreover, the growth behavior for the first 48h under strong winds is associated with growth in fetch-limited conditions. With fetch-limited data being abundant, matching the models here is an indication for “good” behavior of the new physics. For conditions after 48h, we are looking at the transition of wind seas into swells, albeit without the dominant dispersion processes. We have virtually no data in such conditions, and different physical parameterizations behave different in these conditions. Janssen’s approach will result in a rapid decline of wave height initially, and then in slower decline. Tolman and Chalikov will result in a much slower but sustained loss of wave energy. Without us knowing what is actually happening in nature, there is limited value in being able to reproduce a specific model in these conditions.
- Tuning allows for getting the right mean wave parameters. Tuning has less impact on / control over spectral shapes. A more convincing argument that the new physics parameterizations are good or “better” would be to show that spectral shapes are realistic, and to show how, for instance, these new physics reproduce the equilibrium range of the spectrum
Section 4 presents a discussion. I felt this was a little out of place. I would have preferred an assessment of why the new parameterizations are better and include an assessment or recognition of some of my questions and comments provided above here.
Section 5 represents conclusions. At the present, I find the conclusions weak and poorly founded in the results. Please note that these comments are a critique on the presentation of the results. I do believe that there is value in the more rigorous derivation of the parametric expressions. The numbering below refers to the subsequent paragraph in this section.
- I do not understand the first paragraph; What does the word “vulnerable” imply? “excessively” is highly subjective, what is the metric of a formulation (old or new) being “excessively” parameterized.
- I can agree with the general statements in this paragraph, but no theory in these environmental sciences is able to stand on its own without hard observational validation. The observational validation presented here is tentative at best.
- The third paragraph presents the main conclusions of the study, with dissipation terms (15) and (20)+(26). The third paragraph then discusses the first of these source terms. The dissipation term (15) contains a scaling factor for which the authors claim a valid range of an order of magnitude. Such uncertainty does not agree with the statement that their results “… represents definitely ...” the process they seek to describe. The lack of spectral validation of the source term and resulting spectra also is not consistent with this claim.
- The fourth paragraph discusses the second source term and claims that the results show that the turbulent dissipation is dominant and essential for wave modeling. I mentioned above the uncertainty in wave growth formulations, and that wave growth is driven by the small difference between growth and dissipation. The present results therefore do not conclusively address if the second dissipation term is physically dominant or is needed here to counterbalance a potential overestimation of the input source term with which it is used.
- I do like the forward look in the fifth paragraph and agree that it would be interesting to take this work forward (an implicitly that the present results are ultimately publishable).
Some additional comments and questions:
Line 19: “other” Other than what is meant here? If you mean that that the dynamical equations lead to the nonlinear interaction source term, then that needs to be called out before you talk about other source terms.
Lines 50-35. Please provide a foundational journal reference to WW3 like you did with WASNUM. Now you are only referring to separate research done with WW3 by users and a manual.
Lines 71-72: Tolman and Chalikov us a dissipation expression that is equivalent to a turbulent dissipation to get a tunable closure term. They explicitly state that this should not be interpreted as them attributing wave energy dissipation to oceanic turbulence.
Lines 79-83: What is the “third” frequency range in Tolman and Chalikov? If the authors refer to the smooth transition between the low- and high-frequency dissipation mechanisms, then it is a stretch to call this a separate regime. If this is referring to the parametric tail used in wave models, then that should be mentioned with the original Komen et al reference where it was first used.
Derivations leading up to Eq. (15) on line 220: Please define what upper-case K and lower-case k are relative to the wave number vector and its components, as well as upper case K hat and K0.
Lines 409-411: There are three different source term packages mentioned here. It is not clear from the text which input source term has been used with the new dissipation source terms. Please elaborate.
Citation: https://doi.org/10.5194/egusphere-2025-2671-RC1 -
AC1: 'Reply on RC1', Meng Sun, 17 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2671/egusphere-2025-2671-AC1-supplement.pdf
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RC2: 'Comment on egusphere-2025-2671', Anonymous Referee #2, 15 Aug 2025
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AC2: 'Reply on RC2', Meng Sun, 17 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2671/egusphere-2025-2671-AC2-supplement.pdf
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AC2: 'Reply on RC2', Meng Sun, 17 Sep 2025
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Yongzeng Yang
Fuwei Wang
Meng Sun
Xingjie Jiang
Xunqiang Yin
Yongfang Shi
Yong Teng
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(3473 KB) - Metadata XML
Review of "Analytical approaches for wave energy dissipation induced by wave generated turbulence and random wave-breaking” by Yang et al., manuscript egusphere-2025-2671 (my first review of this manuscript).
The authors present an interesting and detail assessment of wave energy dissipation in wind wave models. The paper is easily understandable but would benefit from editing by native English speakers.
The authors provide an extensive review of previous literature in the introduction. I applaud the authors for the completeness of the review, even though that resulted in a rather long introduction. The discussion of the linkage between oceanic turbulence and wind wave dissipation starts at line 62 with the references to Polnikov’s work and takes us through subsequent theoretical and practical understanding of these processes with many more references. The authors observe the lack of theoretical / mathematical foundation for the existing models and set forth to provide a more solid mathematical background for the link between ocean turbulence, random wave breaking and wave energy dissipation.
The next section deals with theoretical / mathematical derivations. Section 2.1 addresses the linkage between wave-generated turbulence and wave energy dissipation, culminating in Equation (15) for wave energy dissipation associated with oceanic wave-generated turbulence. The authors then compare their dissipation with wave growth formulations, where they appear to imply without saying as much that either the two source terms need to be in close balance, and/or that the balance between the two is what governs overall growth rates. It does not address the uncertainty in both terms. The old Large and Pond assessment that the uncertainty in wave growth rates from observations have an uncertainty of up to an order of magnitude, in my opinion, still holds. The comparison between dissipation rates (e.g., Fig. 3) is fairly convincing in that the bulk rates are similar as one would expect from the fact that the derivation assumes a close linkage. What is missing here or later in the paper is how (15) compares to previous formulations, and why / how it is better. Note that if it is the same, the more rigorous derivation might still fully justify publication.
Section 2.2 then addresses the second dissipation process associated with wave breaking (I assume mostly at the crest of at the dominant waves), culminating in a fairly traditional source term formulation (20) with a new dissipation coefficient (26). On line 355 Eq. (26) is introduced as “Hence we propose an improved attenuation coefficient expressed as follows”. As with the expression for the first mechanism, there is no direct comparison to previous formulations. Whereas this may be a new formulation, there is no proof presented why this is “improved”, unless one accepts that a more rigorous derivation can be considered as improved for a wave model that overall is still highly empirical. Moreover, I do not find the comparisons with observations in Figures 5 and 6 overly convincing, mostly due to the signal to noise ratio in the data.
What interests me most as a practical wave modeler, is if the new formulations show new scaling behavior compared to previously suggested models, and if they introduce new functional dependencies within the processes described here.
In Section 3 the authors apply their new sources terms in a numerical model and provide results of model integration in spatially homogeneous conditions (duration-limited growth), providing comparisons with a physics set-up of the WAM Cycle 4 model (i.e., Janssen 1994). I find this the weakest part of the manuscript for the following reasons.
Section 4 presents a discussion. I felt this was a little out of place. I would have preferred an assessment of why the new parameterizations are better and include an assessment or recognition of some of my questions and comments provided above here.
Section 5 represents conclusions. At the present, I find the conclusions weak and poorly founded in the results. Please note that these comments are a critique on the presentation of the results. I do believe that there is value in the more rigorous derivation of the parametric expressions. The numbering below refers to the subsequent paragraph in this section.
Some additional comments and questions:
Line 19: “other” Other than what is meant here? If you mean that that the dynamical equations lead to the nonlinear interaction source term, then that needs to be called out before you talk about other source terms.
Lines 50-35. Please provide a foundational journal reference to WW3 like you did with WASNUM. Now you are only referring to separate research done with WW3 by users and a manual.
Lines 71-72: Tolman and Chalikov us a dissipation expression that is equivalent to a turbulent dissipation to get a tunable closure term. They explicitly state that this should not be interpreted as them attributing wave energy dissipation to oceanic turbulence.
Lines 79-83: What is the “third” frequency range in Tolman and Chalikov? If the authors refer to the smooth transition between the low- and high-frequency dissipation mechanisms, then it is a stretch to call this a separate regime. If this is referring to the parametric tail used in wave models, then that should be mentioned with the original Komen et al reference where it was first used.
Derivations leading up to Eq. (15) on line 220: Please define what upper-case K and lower-case k are relative to the wave number vector and its components, as well as upper case K hat and K0.
Lines 409-411: There are three different source term packages mentioned here. It is not clear from the text which input source term has been used with the new dissipation source terms. Please elaborate.