# Orifice versus Converging-Nozzle Grid Turbulence: A Wavelet Perspective
## 1 Introduction  
Homogeneous isotropic turbulence is the simplest form of turbulence. A passive grid or perforated plate has been widely employed as a turbulence generator to achieve a nearly homogeneous isotropic flow. The ground-breaking work of [PERSON] [1] paved the path for a long series of grid turbulence studies. [PERSON] [2] and [PERSON] [3, 4] were among the first who studied isotropic turbulence and its decay by passing a uniform stream through a grid. Grid-induced turbulence can be divided into different regimes, each with its own unique set of flow characteristics [5, 6]. Immediately downstream of the grid, a highly anisotropic and inhomogeneous turbulence-developing zone forms from the jet-wake interactions. Turbulent eddies develop as a result of the shearing flow produced by the predominant jet-wake interplay present in this region. The flow nearly resembles homogeneous characteristics farther downstream of the grid, identified as the initial decay region. The decay is predominantly caused from the faster dissipating smaller eddies, leaving the slower decaying large-scale structures nearly unaffected. This is followed by the final decay region in the absence of the smaller eddies, surviving with a truncated turbulence cascade of large eddies directly dissipating via viscosity. Detailed investigations on grid-generated turbulence inside a wind tunnel carried out by [PERSON] and [PERSON] [7] revealed that the flowbeyond the developing region downstream of the grid is nearly isotropic, making grids a suitable isotropic turbulence generator. Several studies have been conducted utilising traditional statistical methods to understand the effects of various determinants such as grid geometry (also known as upstream conditions), initial flow parameters, and turbulence length scales, all of which are known to influence the properties and subsequent decay of the resulting grid turbulence. [PERSON] and [PERSON] [8] studied the decay of turbulence using biplane grids, inclined rod grids, and honeycomb grids, concluding that the isotropy level and distribution of energy-containing eddies varies significantly with grid geometry and the measured decay remains essentially constant during turbulent dissipation. [PERSON] et al. [9] showed that the pressure drop across the turbulence generator is the primary energy source for the turbulent flow downstream of the grid wherein the turbulence intensity increases with the plate/grid solidity within a certain range. [PERSON] et al. [10] utilised a square-mesh grid as a turbulence generator inside a water channel. They carried out turbulent dissipation estimation using particle image velocimetry and Laser Doppler velocimetry techniques alongside substantiating the role of inter-scale dependencies, viscous corrections due to the low Reynolds numbers, and flow inhomogeneity on the measurement bias of dissipation rates. A fundamental comparative study investigating the development of isotropic flow produced behind perforated plates with sharp-edged orificed openings (OPPs) and another with straight holes of finite thickness (SHPPs) was carried out in Ref. [11]. An in-depth analysis of turbulence characteristics establishes OPPs as a better generator of high-level turbulence primarily due to well-defined flow separation. Additionally, there is a negative streamwise autocorrelation for OPPs as opposed to SHPPs where the function is entirely non-negative, implying that the large-scale structures present past the two perforated plates differ qualitatively. These studies clearly establish grid geometry and configuration as one of key factors affecting flow isotropy, turbulence structure, and their decay. Coherent structures such as jets, wakes, and boundary layers are a common feature in many turbulent flows. These coherent structures and their interactions are the underlying reasons for the production and dissipation of flow turbulence [12; 13; 14].