# Orifice versus Converging-Nozzle Grid Turbulence: A Wavelet Perspective
## 1 Introduction
While statistical descriptions of turbulence help us understand the overall characteristics of irregular flow, they do not account for the coherent structures present in the flow which play an integral role in time and space intermittency of turbulence. Wavelet analysis is an effective technique in scrutinizing these localised coherent structures present in the flow. Wavelet analysis was first employed to analyse homogenous turbulent flow by [PERSON] [15] and [PERSON] [16] in the early 1990s subsequent to the introduction of the concept of wavelet transform by [PERSON] [17] and [PERSON] [18] in the 1980s. Wavelet transform can be adopted to decompose the original signal based on frequencies or scales, allowing simultaneous time (or spatial) and frequency domain analysis [19]. Wavelet analysis is primarily classified into continuous wavelet transform (which is performed in a smooth continuous fashion, i.e., using the continuous wavelet function) and discrete wavelet transform (which is carried out in discrete steps, i.e., using the discrete orthogonal wavelet basis function). Many researchers have deployed wavelet transform in multifarious applications, such as for examining turbulence homogeneity at different scales [20], or to analyse turbulent wakes and jets [21; 22], or to detect and characterise coherent structures [23]. [PERSON] [24] developed an orthogonal wavelet multi-resolution technique based on the discrete wavelet transform that enabled an event in the signal to be decomposed into several events with fine details. Apart from differentiating the coherent and incoherent turbulent structures, the technique is potentially capable of decomposing and characterizing them quantitatively based on their characteristic frequencies (or scales) in the time domain. [PERSON] et al. [25; 26] employed a wavelet multi-resolution technique for detecting spatial structures of different scales by assessing the results from the particle image velocimetry measurements of unsteady flow. [PERSON] et al. [27; 28] conducted an experimental study to capture details of wake flow structures formed behind a wall-mounted short cylinder. They utilised wavelet transforms to decompose the three-component vorticity data of cylinder wakes into several wavelet components according to their central frequencies to disclose multi-scale flow structures around the cylinder, such as the dominant large-scale structures in the near-wake region, intermediate-scale streamwise and trailing vortices, and the small-scale structures farther downstream formed by the breakdown of large- and intermediate-scale vortices. [PERSON] et al. [29] used a two-dimensional continuous wavelet transform to study the near-wall turbulence intermittency by decomposing the flow field into intermittent and non-intermittent parts based on local Reynolds stress and flatness factor. They concluded that away from the wall, the intermittent part has a smaller scale and possesses a minor portion of the total turbulent energy, whereas both the intermittent and non-intermittent parts possess an almost similar magnitude and scale close to the wall. More recently, [PERSON] et al. [30] combined the capabilities of wavelet transform and the proper orthogonal decomposition to reveal the turbulent wake generated by a triangular cylinder. They concluded that the length scale of wavelet components decreased with rising frequency, indicating the potential of frequency analysis to understand the spatial-related length scale of vortices. In addition, the wavelet transforms can be used to further delineate turbulent structures with different scales. In short, the wavelet decomposition technique is a promising tool for studying multi-scale turbulence structures. Taking advantage of wavelet analysis, the current study extends our previous work on perforated-plate-induced turbulence in a wind tunnel [31], furthering the revelation of the eddying motions in the flow.