Two-particle diffusion in homogeneous turbulence with stable stratification by linear RDT spectral space analysis and application of a simplified model

This paper investigates the numerical study of relative two-particle diffusion in homogeneous stably stratified turbulence. The focus is on obtaining components of tensors Delta(t ',t) and Delta r(t)which are associated with oneparticle and two-particle diffusion, respectively. This is achieved by utilizing Lagrangian two-time velocity -> correlations for both individual particles and two particles initially separated by delta x0. To facilitate the analysis, a simple two-particle diffusion model is developed based on assumptions similar to previous works by Kaneda and Ishida, as well as Ishihara and Kaneda, to elaborate one-particle and two-particle diffusion models. Using this model, Lagrangian two-time velocity correlations are calculated from numerically obtained two-time correlations spectra using a linear analysis RDT (rapid distortion theory) or the so-called rapid distortion approximation in the spectral space. The components of the two-particle diffusion tensor are then deduced directly. This study employs linear solutions of the Navier-Stokes equations using the Boussinesq approximation to describe stably stratified turbulence. The application of this two-particle diffusion model considers an initial turbulence with a Reynolds number R lambda = 2022.80 associated with the Taylor micro-scale of 2022.80. In this article, a large Reynolds number (RL = 270,957) was chosen to study the characteristics of homogeneous stably stratified turbulence. The choice of a large Reynolds number allows for the investigation of turbulence at smaller scales and provides a more detailed understanding of the flow dynamics. Two values of the Froude number (Fr) are selected: Fr=0.0026 and Fr=0.0045, in accordance with previously adopted criteria. Additionally, different values of the vertical displacement delta x0/eta are chosen, where (eta) represents the Kolmogorov length-scale. Ultimately, two numerical simulation series are conducted: R lambda =2022.80, Fr=0.0045, delta x0/eta=15, 17, 20, 24 and R lambda =2022.80, Fr=0.0026, delta x0/eta=15, 20, 25. The primary objective of this study is to delve into the fundamental problem of highlighting the t3 Richardson law and the 4/3 diffusivity Richardson law in the horizontal plane during the intermediate range of times, focusing on two-particle diffusion.