This paper addresses the challenges associated with the numerical simulation of stratified flows. The problem is described by the Boussinesq approximation of the Navier-Stokes equations and it is discretized by the Finite Element Method (FEM). For the discretization, the Taylor-Hood (TH) finite element is used for the approximation of the velocity-pressure couple and density perturbation is approximated by quadratic elements. The numerical scheme is implemented by in-house solvers and obtained numerical results are compared to the available reference data.