## 3 Analysis Results  
### Global Wavelet Spectra (WPS)  
In this study, we use the GWS estimates (Equation (3)) to examine the power spectral characteristics of internal waves according to depths. To test the significance of the GWS estimates, we use 1000 surrogate time series generated via a simple AR-1 process as a red noise describing the oceanic background field [43], given by  
\[x_{t}=\alpha x_{t-1}+\epsilon_{t} \tag{10}\]  
where \(\alpha\) represents the lag-1 autocorrelation of temperature anomaly series at each depth, and \(\epsilon_{t}\) is taken from Gaussian white noise. As shown in Figure 3, the oscillatory patterns of temperature anomalies seem to be distinct for two durations, the first duration (from 9/09 to 9/13) and the second duration (from 9/14 to 9/18). Thus, we compute GWS estimates separately for both periods and name them as the inner and outer centers of the eddy because the target eddy slowly migrated during the glider's virtual mooring observations. The GWS estimates for both domains are presented in Figure 5 (inner center) and Figure 6 (outer center). The red dotted lines indicate the critical values satisfying a 95% significance level of the GWS distribution obtained from a surrogate ensemble consisting of 1000 time series generated via the AR1 process. All power estimates were scaled to the range of [0, 1] for comparison purposes by dividing by the maximum power value. Figure 5: The global wavelet spectra (GWS) estimates of temperature anomalies at 25 depths in the inner center. Black and green vertical dotted lines indicate the semidiurnal and diurnal periods, respectively. Figure 6: Same as Figure 5 except for the outer center. As shown in Figures 5 and 6, the internal tides (DIT, diurnal internal tide; SIT, semidiurnal internal tide) are relatively dominant; the power of DITs is greater than that of SITs. The dominance of DIT over SIT is consistent with the fact that the study site is located approximately 1000 km eastward from the Luzon Strait, which is a representative generation site of internal tides. Further, [PERSON] [44] showed that the study site is significantly influenced by prevailing east-ward propagating DITs from the Luzon Strait. Based on these observational facts, we construct wavelet-coherence networks corresponding to diurnal and semidiurnal periods in the following analysis. The difference in power spectral patterns between both domains (inner and outer centers) is clearly seen in the upper layer (above 400 m), while it greatly decreases in the lower layer (below 400 m), strongly indicating that the oceanic environments between the upper and lower layers are different. Also, the difference in power spectral patterns between the upper and lower layers is more dramatic in the inner center (Figure 5) than in the outer center (Figure 6), indicating that the oceanic environments between the inner and outer centers are different. From these GWS analyses, we can identify two key observations regarding the structure and the influence of a mesoscale eddy on modulating internal tides. Firstly, a complex power spectral pattern is distinctly observed at depths between 50 and 320 dbar in the inner center (Figure 5), suggesting that the modulation of internal tides is actively taking place due to the significant impact of the investigated mesoscale eddy. In comparison to their behavior in the lower layer (below 400 dbar), the spatial extent of interactions between internal tides and the mesoscale eddy appears to be limited in the upper layer, indicating that the examined mesoscale eddy is primarily intensified near the surface. Secondly, the power spectral patterns observed in the outer center (Figure 6) are comparatively moderate when contrasted with those in the inner center, and they do not exhibit a significant difference between the upper and lower layers. This observation suggests that the mesoscale eddy's influence on internal tide modulation is primarily concentrated in the upper layer of the inner center.