Journal of Applied Fluid Mechanics1735-357212120190101Numerical Analysis of Homogeneous and Stratified Turbulence under Horizontal Shear via Lagrangian Stochastic Model: Richardson Number Effect9510275110.29252/jafm.75.253.28840ENL. ThamriUniversity of Tunis El-Manar, Faculty of Sciences of Tunis, Department of Physics, TunisiaT. NaffoutiUniversity of Tunis El-Manar, Faculty of Sciences of Tunis, Department of Physics, TunisiaM. BouzaianeLaboratoire de Mécanique des Fluides et des Transferts Thermique, TunisiaJournal Article19700101The present investigation is carried out to reveal Richardson number (Ri) effects on an homogeneous and stratified turbulence under horizontal shear. The problem is simulated via Lagrangian Stochastic model (LSM). Hence, the method of Runge Kutta with fourth order is adopted for the numerical integration of three differential systems under non linear initial conditions of Jacobitz (2002) and Jacobitz et al. (1998). This study is performed for Ri ranging from 0.2 to 3.0. It has been found that computational results by the adopted model (LSM) gave same findings than that of preceding works. It has been shown a global tendency of different parameters governing the problem to equilibrium asymptotic states for various values of Ri. The comparative study between the computations of the present LSM and direct numerical simulation of Jacobitz demonstrates a good agreement for both methods for the ratios of; potential energy Kθ/E and kinetic energy K/E toward the total energy E and the principal component of anisotropy b12 It has been found that Ri is the most important parameter affecting the thermal and dynamic fields of the flow. Hence, increase Ri conduct to increase the uniform stable stratification and decrease for the uniform mean shear S. It can be concluded that Ri is a main non-dimensional parameter which enable us to understand physical phenomenons produced inside stratified shear flows.https://www.jafmonline.net/article_751_f9b9e8a44d1eaaf0007ab26fc1b782a3.pdf