The work is devoted to direct numerical simulation of turbulent mixing by shear driven instability at an interface of two plane-parallel gas flows. The work presents the results obtained in 2D simulations of turbulence being developed at the interface of two almost incompressible gases using the MAX program package. Spatial and temporal evolution of the turbulence zone resulted from shear driven instability is studied. We calculated the constant of shear driven turbulence mixing and investigated how the rate of turbulence zone growth depended on density difference of mixed fluids. Heterogeneity coefficient of the mixture was calculated for all considered density differences.