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.

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.