Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea

Fan, Liming; Sun, Hui; Yang, Qingxuan; Li, Jianing

doi:https://doi.org/10.5194/egusphere-2023-1914

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https://doi.org/10.5194/egusphere-2023-1914

Preprints

14 Sep 2023

| 14 Sep 2023

Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea

Liming Fan, Hui Sun, Qingxuan Yang, and Jianing Li

Abstract. We investigate interaction between an anticyclonic eddy (AE) and semidiurnal internal tide (SIT) on the continental slope of the northeastern South China Sea (SCS), using a high spatiotemporal resolution numerical model. Two key findings are as follows. First, the AE promotes energy conversion from low-mode to higher-mode SIT; additionally, production terms indicate that the energy is also transferred from the SIT field to the eddy field at an average rate of -3.0 mW m^-2. Second, the AE can modify the spatial distribution of tidal-induced dissipation by both refracting and reflecting low-mode SIT. The phase and group velocities of the SIT are significantly influenced by the eddy field, resulting in a shift of the internal tidal rays to the north or south. These findings deepen our understanding of complex interactions between AE and SIT and of their impacts on energy conversion, wave propagation, and coastal processes.

Received: 01 Sep 2023 – Discussion started: 14 Sep 2023

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Journal article(s) based on this preprint

21 Feb 2024

Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea

Liming Fan, Hui Sun, Qingxuan Yang, and Jianing Li

Ocean Sci., 20, 241–264, https://doi.org/10.5194/os-20-241-2024,https://doi.org/10.5194/os-20-241-2024, 2024

Short summary

Liming Fan, Hui Sun, Qingxuan Yang, and Jianing Li

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1914', Anonymous Referee #1, 07 Oct 2023

Review of “Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea” by Fan et al.
Based on the MITgcm LLC4320 data, this paper investigates the interaction between semidiurnal internal tide (SIT) and an anticyclonic eddy (AE) in the northern South China Sea. Through calculating the energy budget of the first three modes of SIT, the authors analyze the interaction between the modal SIT and AE. Results indicate that the AE can modulate the intensity and propagation of SIT. The followings are my comments on this paper.
L13, As the authors have pointed out that the energy is transferred from SIT to AE, the value of the transferring rate (-3.0 mW m^-2) should be changed to 3.0 mW m^-2.
L77-79, “The model can effectively simulate free propagating internal waves such as ITs, while regional models cannot because of …”. I disagree.
L109-110, I do not understand why model decomposition is related to horizontal resolution.
L117 and Figure 1, The regionally averaged barotropic tidal currents do not make sense, because the phases of tidal currents at different points are different.
L135, Please introduce how to calculate the HKE and APE.
L163-165, The authors use the theoretical estimation of Vic et al. and L_1 of Xu et al. to demonstrate that the simulated mode-2 SIT is consistent with the theory (Figure 3). However, it seems that the simulated mode-1 SIT (Figure 2) is not consistent with L_1 of Xu et al. Moreover, it seems that the calculated L_3 (L178) is not consistent with the result shown in Figure 4.
Figure 6. If the IT is locally generated, the corresponding conversion from barotropic tides (C_0x, x=1,2,3,…) should be positive. If the local IT is influenced by that propagated from remote source, the value of conversion might be negative. It is generally recognized that high-mode IT cannot propagate a long distance from the source. To be specific, high-mode IT (especially mode-4 and mode-5) generated at the Luzon Strait might not reach the study region. Therefore, how to explain the negative values of C_04 and C_05?
Section 3.2.1 and corresponding content in section 3.1.1, The authors find that the calculated r_E is different from the theoretical r_E for mode-2 SIT and speculate that it is caused by the interference of SIT after a reflection at the continental slope. Hence, they analyze the reflection of mode-2 SIT in section 3.2.1. I have several questions for this analysis. First, if mode-2 SIT is reflected at the slope, mode-1 and mode-3 SITs are also reflected at the slope. Why only mode-2 SIT causes interference as well as a r_E different from the theoretical value? Second, as shown in Figure 11, the incoming and reflected energy fluxes are in different directions, how to form interference in this case?
Figure 11a, Compared with previous studies (e.g. Kerry et al., 2013; Xu et al., 2021), the energy flux pattern of SIT shown in this study is odd.
L322-326, The authors find that the reflected mode-2 SIT on day 151 is larger than that on day 137, and then conclude that the AE promotes the reflection of SIT. This is imprecise, because the incoming SIT is also increased from day 137 to 151 (section 3.1.1).
L347, There is no c^U in Equation (6).
L350, There is no c in Equation (7).
Reference
Kerry, C.G., Powell, B.S., Carter, G.S., 2014. The impact of subtidal circulation on internal tide generation and propagation in the Philippine Sea. J. Phys. Oceanogr. 44, 1386–1405. https://doi.org/10.1175/JPO-D-13-0142.1.
Xu, Z., Wang, Y., Liu, Z., McWilliams, J. C., & Gan, J., 2021. Insight into the dynamics of the radiating internal tide associated with the Kuroshio Current. J. Geophys. Resear.:Oceans, 126, e2020JC017018, doi: 10.1029/2020JC017018.

Citation: https://doi.org/10.5194/egusphere-2023-1914-RC1
- AC1: 'Reply on RC1', Hui Sun, 04 Nov 2023
  
  We appreciate the reviewer's insightful comments, which have greatly aided us in improving our manuscript. We have made an effort to address each of your comments. Since some equations are involved, we included all our responses in the Supplement for a clearer view. We look forward to your further comments.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1914-AC1
RC2:
'Comment on egusphere-2023-1914', Anonymous Referee #2, 15 Oct 2023

Review of ``Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea'' by Fan et al.
This study examines data from high resolution numerical simulations, focusing on the northeastern South China Sea which experiences internal tides propagating from their generation site at the Luzon Straits. A short period of just under 3 spring-neap tidal cycles is considered, and the internal tide energy fluxes are compared between two periods 2 weeks apart, one of which includes an anticyclonic mesoscale eddy, while the other has no eddy. This comparison reveals that there is a net transfer of energy from the internal tides to the eddy (at least when only the first 3 modes are considered) and that the eddy facilitates topographic conversion from mode 1 to higher modes. The role of the eddy in refracting the internal tide energy flux is also considered, and in affecting changes in reflection at the continental slope. Overall, while this manuscript examines only one instance of internal tide/mesoscale eddy interaction, there are nonetheless many interesting results. However, I recommend some more effort to explain the causes of some of the behavior, and more connection made between the different changes identified.
Significant suggestions
1. Energy transfer from internal tide to eddy, v. inter-modal energy transfer.
From eqn 1, the authors have identified a net energy transfer from the internal tide to the eddy. However, it would be of interest to know whether this is manifest in an increase in eddy energy, or whether there a subsequent energy transfer from the eddy to higher internal tide modes. Can you separately diagnose the net mode-mode transfer, as in https://doi.org/10.1175/JPO-D-23-0045.1? Or can you track the eddy energy tendency - does the eddy energy in fact increase due to the internal tide energy transfer?
2. Energy flux arrows
It would be very helpful to see arrows showing the energy flux in the figures 2a-c, 3a-c, and 4a-c. Which direction is the internal tide energy coming from? For example, is mode 1 predominantly coming from the Luzon Straits, while mode 3 is coming from the local continental slope, due to the topographic conversion from mode 1 to 3?
3. How does the presence of the eddy contribute to the enhanced topographic scattering from mode 1 to higher modes?
Can we connect the enhanced topographic scattering in figures 5 and 6 to the influence of the eddy on the mode 1 propagation shown in figure 14? Does the redirection of the mode 1 toward the slope lead to the increase topographic energy conversion from mode 1 to higher modes?
4. Reflection at continental slope - mode 1
In section 3.2.1 the impact of the eddy on the reflection of mode 2 is examined. However, mode 1 is not mentioned here - why not? It would be interesting to know whether the increased topographic conversion from mode 1 to higher modes in the presence of the eddy also leads to reduced reflection of mode 1.
5. Reasons for enhanced reflection of mode 2
While the authors have shown that the eddy leads to enhanced reflection of mode 2 at the slope, I don't see much explanation of this change - how does the eddy influence this enhanced reflection? Is it due to the refraction of the internal tide toward the slope? Or is it due to the changes in stratification structure induced by the eddy influencing the slope criticality?
Minor comments
Abstract, line 13-14: The rate at which energy is transferred from the internal tide to the eddy is given here. To know how significant this is, what is this transfer rate as a percentage of the incoming energy flux integrated over the eddy diameter/height?
Introduction, line 25: delete "and so on", since it does not provide any additional information.
Line 33: More correctly, it is not the dissipation which affects the overturning circulation, but rather the mixing that may be induced by the loss of energy from internal tides.
Line 37: "a hotspot" - a hotspot of what?
Line 41-42: If transfer of energy from the mesoscale eddy to the internal wave field induces a viscous effect, this would be a viscous effect on the eddy circulation, not on the internal wave field (which increases in energy in this statement). So it's doubtful that an eddy viscosity can be used to parameterize this effect in an internal tide prediction model.
Line 51 and elsewhere: Change "inner-modal redistribution" to "inter-modal redistribution" (it is a redistribution between modes).
Figure 7, caption: Change "but for the advection term of the velocity component.." to "but for the velocity component of the advection term..."
Figure 8, caption: Change "but for the advection term of the pressure component.." to "but for the pressure component of the advection term.."
Lines 317-325: There is some repetition here. For example line 322-323 closely repeats line 317-318.
Line 334-335, and elsewhere: "near-filed" and "far-filed" should be "near-field" and "far-field".
P18, lines 362-368: Too much space is given here to showing that the stratification changes alone have little impact on the ray propagation. I think you could combine figures 13 and 14 and focus on discussing the more significant impact of the eddy flow field.

Citation: https://doi.org/10.5194/egusphere-2023-1914-RC2
- AC2: 'Reply on RC2', Hui Sun, 04 Nov 2023
  
  We appreciate the reviewer's insightful comments, which have greatly helped us in improving our manuscript. We have made an effort to address each of your comments. For a clearer view, we included all our responses in the Supplement. We look forward to your further comments.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1914-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1914', Anonymous Referee #1, 07 Oct 2023

Review of “Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea” by Fan et al.
Based on the MITgcm LLC4320 data, this paper investigates the interaction between semidiurnal internal tide (SIT) and an anticyclonic eddy (AE) in the northern South China Sea. Through calculating the energy budget of the first three modes of SIT, the authors analyze the interaction between the modal SIT and AE. Results indicate that the AE can modulate the intensity and propagation of SIT. The followings are my comments on this paper.
L13, As the authors have pointed out that the energy is transferred from SIT to AE, the value of the transferring rate (-3.0 mW m^-2) should be changed to 3.0 mW m^-2.
L77-79, “The model can effectively simulate free propagating internal waves such as ITs, while regional models cannot because of …”. I disagree.
L109-110, I do not understand why model decomposition is related to horizontal resolution.
L117 and Figure 1, The regionally averaged barotropic tidal currents do not make sense, because the phases of tidal currents at different points are different.
L135, Please introduce how to calculate the HKE and APE.
L163-165, The authors use the theoretical estimation of Vic et al. and L_1 of Xu et al. to demonstrate that the simulated mode-2 SIT is consistent with the theory (Figure 3). However, it seems that the simulated mode-1 SIT (Figure 2) is not consistent with L_1 of Xu et al. Moreover, it seems that the calculated L_3 (L178) is not consistent with the result shown in Figure 4.
Figure 6. If the IT is locally generated, the corresponding conversion from barotropic tides (C_0x, x=1,2,3,…) should be positive. If the local IT is influenced by that propagated from remote source, the value of conversion might be negative. It is generally recognized that high-mode IT cannot propagate a long distance from the source. To be specific, high-mode IT (especially mode-4 and mode-5) generated at the Luzon Strait might not reach the study region. Therefore, how to explain the negative values of C_04 and C_05?
Section 3.2.1 and corresponding content in section 3.1.1, The authors find that the calculated r_E is different from the theoretical r_E for mode-2 SIT and speculate that it is caused by the interference of SIT after a reflection at the continental slope. Hence, they analyze the reflection of mode-2 SIT in section 3.2.1. I have several questions for this analysis. First, if mode-2 SIT is reflected at the slope, mode-1 and mode-3 SITs are also reflected at the slope. Why only mode-2 SIT causes interference as well as a r_E different from the theoretical value? Second, as shown in Figure 11, the incoming and reflected energy fluxes are in different directions, how to form interference in this case?
Figure 11a, Compared with previous studies (e.g. Kerry et al., 2013; Xu et al., 2021), the energy flux pattern of SIT shown in this study is odd.
L322-326, The authors find that the reflected mode-2 SIT on day 151 is larger than that on day 137, and then conclude that the AE promotes the reflection of SIT. This is imprecise, because the incoming SIT is also increased from day 137 to 151 (section 3.1.1).
L347, There is no c^U in Equation (6).
L350, There is no c in Equation (7).
Reference
Kerry, C.G., Powell, B.S., Carter, G.S., 2014. The impact of subtidal circulation on internal tide generation and propagation in the Philippine Sea. J. Phys. Oceanogr. 44, 1386–1405. https://doi.org/10.1175/JPO-D-13-0142.1.
Xu, Z., Wang, Y., Liu, Z., McWilliams, J. C., & Gan, J., 2021. Insight into the dynamics of the radiating internal tide associated with the Kuroshio Current. J. Geophys. Resear.:Oceans, 126, e2020JC017018, doi: 10.1029/2020JC017018.

Citation: https://doi.org/10.5194/egusphere-2023-1914-RC1
- AC1: 'Reply on RC1', Hui Sun, 04 Nov 2023
  
  We appreciate the reviewer's insightful comments, which have greatly aided us in improving our manuscript. We have made an effort to address each of your comments. Since some equations are involved, we included all our responses in the Supplement for a clearer view. We look forward to your further comments.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1914-AC1
RC2:
'Comment on egusphere-2023-1914', Anonymous Referee #2, 15 Oct 2023

Review of ``Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea'' by Fan et al.
This study examines data from high resolution numerical simulations, focusing on the northeastern South China Sea which experiences internal tides propagating from their generation site at the Luzon Straits. A short period of just under 3 spring-neap tidal cycles is considered, and the internal tide energy fluxes are compared between two periods 2 weeks apart, one of which includes an anticyclonic mesoscale eddy, while the other has no eddy. This comparison reveals that there is a net transfer of energy from the internal tides to the eddy (at least when only the first 3 modes are considered) and that the eddy facilitates topographic conversion from mode 1 to higher modes. The role of the eddy in refracting the internal tide energy flux is also considered, and in affecting changes in reflection at the continental slope. Overall, while this manuscript examines only one instance of internal tide/mesoscale eddy interaction, there are nonetheless many interesting results. However, I recommend some more effort to explain the causes of some of the behavior, and more connection made between the different changes identified.
Significant suggestions
1. Energy transfer from internal tide to eddy, v. inter-modal energy transfer.
From eqn 1, the authors have identified a net energy transfer from the internal tide to the eddy. However, it would be of interest to know whether this is manifest in an increase in eddy energy, or whether there a subsequent energy transfer from the eddy to higher internal tide modes. Can you separately diagnose the net mode-mode transfer, as in https://doi.org/10.1175/JPO-D-23-0045.1? Or can you track the eddy energy tendency - does the eddy energy in fact increase due to the internal tide energy transfer?
2. Energy flux arrows
It would be very helpful to see arrows showing the energy flux in the figures 2a-c, 3a-c, and 4a-c. Which direction is the internal tide energy coming from? For example, is mode 1 predominantly coming from the Luzon Straits, while mode 3 is coming from the local continental slope, due to the topographic conversion from mode 1 to 3?
3. How does the presence of the eddy contribute to the enhanced topographic scattering from mode 1 to higher modes?
Can we connect the enhanced topographic scattering in figures 5 and 6 to the influence of the eddy on the mode 1 propagation shown in figure 14? Does the redirection of the mode 1 toward the slope lead to the increase topographic energy conversion from mode 1 to higher modes?
4. Reflection at continental slope - mode 1
In section 3.2.1 the impact of the eddy on the reflection of mode 2 is examined. However, mode 1 is not mentioned here - why not? It would be interesting to know whether the increased topographic conversion from mode 1 to higher modes in the presence of the eddy also leads to reduced reflection of mode 1.
5. Reasons for enhanced reflection of mode 2
While the authors have shown that the eddy leads to enhanced reflection of mode 2 at the slope, I don't see much explanation of this change - how does the eddy influence this enhanced reflection? Is it due to the refraction of the internal tide toward the slope? Or is it due to the changes in stratification structure induced by the eddy influencing the slope criticality?
Minor comments
Abstract, line 13-14: The rate at which energy is transferred from the internal tide to the eddy is given here. To know how significant this is, what is this transfer rate as a percentage of the incoming energy flux integrated over the eddy diameter/height?
Introduction, line 25: delete "and so on", since it does not provide any additional information.
Line 33: More correctly, it is not the dissipation which affects the overturning circulation, but rather the mixing that may be induced by the loss of energy from internal tides.
Line 37: "a hotspot" - a hotspot of what?
Line 41-42: If transfer of energy from the mesoscale eddy to the internal wave field induces a viscous effect, this would be a viscous effect on the eddy circulation, not on the internal wave field (which increases in energy in this statement). So it's doubtful that an eddy viscosity can be used to parameterize this effect in an internal tide prediction model.
Line 51 and elsewhere: Change "inner-modal redistribution" to "inter-modal redistribution" (it is a redistribution between modes).
Figure 7, caption: Change "but for the advection term of the velocity component.." to "but for the velocity component of the advection term..."
Figure 8, caption: Change "but for the advection term of the pressure component.." to "but for the pressure component of the advection term.."
Lines 317-325: There is some repetition here. For example line 322-323 closely repeats line 317-318.
Line 334-335, and elsewhere: "near-filed" and "far-filed" should be "near-field" and "far-field".
P18, lines 362-368: Too much space is given here to showing that the stratification changes alone have little impact on the ray propagation. I think you could combine figures 13 and 14 and focus on discussing the more significant impact of the eddy flow field.

Citation: https://doi.org/10.5194/egusphere-2023-1914-RC2
- AC2: 'Reply on RC2', Hui Sun, 04 Nov 2023
  
  We appreciate the reviewer's insightful comments, which have greatly helped us in improving our manuscript. We have made an effort to address each of your comments. For a clearer view, we included all our responses in the Supplement. We look forward to your further comments.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1914-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Hui Sun on behalf of the Authors (23 Nov 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (28 Nov 2023) by Mehmet Ilicak

RR by Anonymous Referee #3 (19 Dec 2023)

Suggestions for revision or reasons for rejection

1.Lines 14-15: In the Abstract, the authors say that “the AE can modify the spatial distribution of tidal-induced dissipation by both refracting and reflecting low-mode SIT”; In lines 49-50, they say that “ME mostly modulates the propagation of IT in terms of refraction and scattering”. What is more important, reflecting or scattering?
2.Lines 38-39: The authors say that the internal tide and mesoscale eddy have “comparable horizontal scales”, and then they use the “multiscale” to describe their interaction. There seems to be some inconsistency in the phrases “comparable scales” and “multiscale”.
3.Line 69: "AE" and "SIT" have been defined in the abstract, but they should be defined again in the text. They are a bit abrupt here in line 69.
4.Line 114: There's a small error in the formula of the dispersion relation of linear IWs. Sqrt((N^2-ω^2)/(N^2-f^2)) should be Sqrt((N^2-ω^2)/(ω^2-f^2)).
5.Line 117: The authors say “We selected a period for analysis, corresponding to 131-170 days”. When using TPXO, the data necessarily corresponds to definite dates. Why don't you use the date here corresponding to the TPXO, instead of the number of days in the model? It feels like this would lead to a lot of inconvenience in the author's following description.
6.Line 135: the author do not seem to mention what “red curve ( in Figure 2)” means.
7.Line 168 (Figure 3d-f): The Moon's orbit around the Earth is elliptical, with a change in perigee and apogee, a period of about 27 days. The interval between the three spring tides described in this article is exactly 27 days (137 to 164), which makes one wonder if the change in the energy of the internal tides is related to this 27-day inequality of tide. The data used by the authors are model data and should not include this factor of variation in the equinoctial tide. However, the authors should check the model and rule out this possibility.
8.Line 248: I did not find explanation on mode 0 in Figure 7. Is it the barotropical tide, or AE?
9.Line 251: The word “respectively” seems unnecessary.
10.Lines 268, 535: A “*” indicates ordinary multiplication in computer language, but not in math language. When a “*” is occasionally used in math to denote multiplication, it must be a special defined multiplication, such as convolution. Likewise, expressing powers of 10 in terms of “e” (Line 535, Figure B1) is also not normal in math language. “e” equals 2.71828... in math.
11.Line 359 (Figure 14b-c): The authors use “onshore (Northward)” and “offshore (Southward)” to present the direction of energy fluxes integrated along section S1 and S2. In my view, section S1 is along-shore and the energy integrated along it is cross-shore; section S2 is cross-shore and the energy integrated along it is along-shore
12.Line 374 (Figure 15): Typically, wave rays can be find in the contours of the current speed. But here the contours of the current speed show no clear pattern of the wave rays. I wonder how do the author give the black wave rays in Figure 15?
13.Line 380 (Figure 16c-d): The authors gave two sub-figures to compare topographic steepness parameters for days 137 and 151. Unsurprisingly, they are very similar. In Lines 390-391, the authors talke about the similarity but do not explain why they are so similar. In fact, according to Eq. (3), the difference between the two is only in the stratification, which will not change significantly in just half a month, so the similarity is inevitable. This should have been explained in the text.
14.The article uses a lot of formulas, and some of the math symbols are so similar that it's easy to get confused. For example, “c_n” and “c_p” are the eigen speed and phase speed (Line 412), “C_n” is topographic conversion term usually appears with energy exchange term “P_n” (Line 466), “p_n” is the pressure perturbation (Line 510). Then what’s the meaning of “c_n” (Line517, A4) and “c_m” (Line 512, A3)?
15.Line 517: should the “ω” in Eq. A4 be “ω_n”? The expression of this equation may be related to the modes, I think.

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ED: Publish subject to minor revisions (review by editor) (19 Dec 2023) by Mehmet Ilicak

AR by Hui Sun on behalf of the Authors (28 Dec 2023) Author's response Author's tracked changes Manuscript

ED: Publish as is (05 Jan 2024) by Mehmet Ilicak

AR by Hui Sun on behalf of the Authors (11 Jan 2024) Manuscript

Journal article(s) based on this preprint

21 Feb 2024

Numerical investigation of interaction between anticyclonic eddy and semidiurnal internal tide in the northeastern South China Sea

Liming Fan, Hui Sun, Qingxuan Yang, and Jianing Li

Ocean Sci., 20, 241–264, https://doi.org/10.5194/os-20-241-2024,https://doi.org/10.5194/os-20-241-2024, 2024

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Liming Fan, Hui Sun, Qingxuan Yang, and Jianing Li

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Understanding internal tide generation and propagation is crucial for predicting large-scale circulation and climate change. Internal tides are prone to interacting with background currents with similar spatial scales during propagation. This paper investigates the physical mechanism of the interaction between semidiurnal internal tides and an anticyclonic eddy in the northeastern South China Sea using a numerical model with high spatial and temporal resolution.


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