Eur. Phys. J. Plus (2022) 137: 445
https://doi.org/10.1140/epjp/s13360-022-02659-x

Regular Article

Comparative analysis of coupled second-order models on Shear and Richardson numbers effects on homogeneous and stratified turbulence

¹ Département de Physique, Faculté des Sciences de Tunis, University of Tunis El Manar, Tunis, Tunisia
² Laboratoire d’Energétique et des Transferts Thermique et Massique, El Manar, 2092, Tunis, Tunisia
³ Institut Préparatoire aux Etudes d’Ingénieurs El-Manar, El-Manar, 2092, Tunis, Tunisia
⁴ College of Sciences and Humanities of Dawadmi, Shaqra University, Shaqra, Kingdom of Saudi Arabia

^a thamrilamia@yahoo.fr

Received: 13 November 2021
Accepted: 28 March 2022
Published online: 8 April 2022

Abstract

The main focus of this study is to examine effects of Shear and Richardson numbers on physical characteristics of stratified and homogeneous turbulence via three coupled second-order models. Every model of Launder, Reece and Rodi (LRR), Craft and Launder (CL) and Shih and Lumley (SL) related to the scalar field is coupled with the Speziale, Sarkar and Gatski model (SSG) associated with pressure–strain correlation. Hence, three coupled second-order models of SSG-CL, SSG-SL and SSG-LRR are obtained in order to resolve the considered problem. For various Shear number SK/ε ranging from 2 to 20, all findings are presented for three values of Richardson number Ri = 0.15, 1 and 2 related to low and high stratification. Temporal profiles of the current investigation show a global tendency of different turbulent parameters governing the problem to asymptotic equilibrium states as a function of Shear number. It is found that the growth of Shear number conducts to decrease various equilibriums values of normalized turbulence dissipation, principal component of anisotropy and ratio kinetic energy to total energy, corresponding to (ε/KS)_∞, (b₁₁)_∞, (b₂₂)_∞, (b₂₃)_∞, (b₁₃)_∞ and (K/E)_∞, respectively. Principal component of anisotropy (b₁₂)_∞ and ratio of potential energy to total energy (K_ρ/E)_∞ increase as increasing the Shear number. Numerical simulations via various coupled models demonstrate that the turbulence evolution is found to depend strongly with the variation in Richardson number for different values of Shear number. The increase in Shear number leads to growth values of Reynolds number for different Richardson number using three coupled models. In addition, it is proved a good agreement between predictions via different models and those by Direct Numerical Simulation of Jacobitz (Theor Comput Fluid Dyn 13:171–188, 1999) and by Reynolds averaged Navier–Stokes equations (Pereira and Rocha in J Turbul 10(43):1–35, 2009) for the Reynolds stress anisotropy tensor b_ij.