## 1 _Introduction_
Lastly, it can handle non-periodic or irregularly sampled signals, which are  
Figure 1: A map of SSH (sea surface height) in the northwestern Pacific, including the study region marked by a white cross. The glider was carefully controlled on the surface within an RMS (root-mean square) of 720 m around the designated waypoint, as depicted in the inset. usually problematic for Fourier-based spectral analysis methods. These advantages make wavelet analysis particularly well-suited for analyzing complex, non-stationary, or noisy signals, such as those encountered in oceanic oscillatory phenomena. Complex network theory can be applied to examine the structural variability of a complex system by representing the system as a network of interconnected nodes and  
Figure 2: Time evolution of SSHA (sea surface height anomaly) during observations in the study region, where a black dot denotes the glider’s virtual mooring (VM) location. edges. Nodes represent the components or elements of the system, and edges represent the interactions or relationships between them. By analyzing the network's topology, structure, and dynamics, insights can be gained into the underlying mechanisms governing the complex system's behavior [26]. There are several advantages to using complex network theory in this context. Firstly, it enables the simplification of complex systems into more manageable and understandable structures, revealing patterns, clusters, and interactions. Secondly, network metrics, such as degree distribution, clustering coefficient, and betweenness centrality, can provide quantitative descriptions of the system's structural variability. Thirdly, the community detection algorithm [27; 28] can reveal clusters or modules within the network, corresponding to functionally related components or subsystems within the system, and enhance understanding of the system's organization and interactions. Lastly, it can be extended to study the time-varying structure of complex systems. Based on the advantages of wavelet analysis and complex network methodology, we present a wavelet-coherence-based network methodology to analyze the structural variability of the internal waves system consisting of oscillatory multivariate time series with limited sample sizes and abrupt alterations or non-stationary behaviors. However, there are still potential pitfalls, such as threshold selection and the presence of noise or spurious correlations. We adopt statistical significance testing based on the ensemble of surrogate time series in order to avoid the spuriousness in pair-wise wavelet coherence estimation and arbitrariness in threshold selection. In this study, we make up 100 ensembles of the surrogate time series generated via the iAAWT (iterative amplitude-adjusted continuous wavelet transform) algorithm [29; 30; 31] and obtain critical values satisfying 95% significance level on pair-wise wavelet coherence estimates from those ensembles. If an estimated wavelet coherence is larger than its corresponding critical value, both time series are connected by an edge. In this study, we examine the structural variations of internal tide systems, as an example of oscillatory systems, inside a mesoscale eddy, using our new approach based on a combination of wavelet analysis and complex network theory. The organization of this study is as follows. Section 2 contains the materials and methods. Analysis results are given in Section 3, and Section 4 presents the discussion.