## 1 Introduction  
Turbulence is characterized by chaotic fluid motion as exhibited by apparently random fluctuations in pressure and velocity and represents a highly non-linear dynamic system with variations across both temporal and spatial domains. Thus, modal decomposition of the flow field is crucial for researchers to better understand the nature and dynamics of turbulent flows, particularly the spatiotemporal evolution of coherent structures within the flow, which are responsible for the generation of turbulence [1]. Over the last century, numerous analytical approaches and mathematical tools have been developed to gain deeper insights into the physics of turbulence. Among these, Fourier analysis stands out as one of the oldest and most frequently used methods for the modal decomposition of fluid flows. The literature on this approach is extensive, with numerous papers exploring its applications. To illustrate the longevity and continued relevance of this method, consider two studies that delineate the timeline: [PERSON]'s 1938 paper [2], which utilized Fourier analysis for the time and length scale analysis of flow past a prism, and the more recent work by [PERSON] in 2021 [3], which investigated the dynamics of large and small-scale motions in plane Couette-Poiseuille flow. Proper orthogonal decomposition (POD) is another widely adopted decomposition technique that was introduced to the fluid dynamics community by [PERSON] [4] in 1967. POD decomposes the flow field into spatially orthogonal modes, ordered by energy level, each with a time history characterized by fluctuating components and a frequency spectrum. Since its introduction, POD has been extensively applied in various contexts, including identifying coherent structures [5], controlling flow by manipulating dominant flow structures [6; 7], and developing reduced-order models for complex, computationally intensive flow problems [8; 9]. The other later-developed yet very popular approach involves the use of \"Wavelet Transform\" (WT), originally developed by [PERSON] in 1980 for seismic data analysis [10]. WTs are mathematical tools used to decompose signals into their constituent frequencies, offering both time and frequency localization, which makes them particularly useful for analyzing non-stationary turbulent fluid flows. The use of wavelets in turbulence was first reported by [PERSON] and [PERSON] [11] in their work to analyze a two-dimensional homogeneous turbulent flow field obtained from numerical simulations. Interested readers are directed to the 1992 review paper by [PERSON] [12], which highlights the potential of wavelet transforms (WTs) in fluid dynamics. The paper demonstrates their effectiveness in identifying coherent structures within turbulent flows and discusses some of the initial pioneering works. Papers from [PERSON]'s group laid the groundwork for subsequent research, which has expanded the application of WTs in fluid flow modal decomposition. Recent studies have further advanced the application of wavelet-based techniques to analyze complex flow patterns and enhance the understanding of flow dynamics in various engineering applications (cf. [13; 14; 15] to cite but a few). These contemporary works demonstrate the ongoing evolution and usefulness of the WT approach in extracting meaningful insights from fluid flow data, particularly in addressing the challenges posed by the multi-scale nature of turbulence, turbulence modeling, data-driven turbulence, and the development of reduced order modeling (ROM). In addition, there are efforts that combine the features of both POD and WT to further our understanding of the dynamics of turbulence, as well as applications in the data-driven turbulence approaches. For example, [PERSON] et al.