Coherent vortex extraction using wavelets is applied to a shear-stratified turbulent flow computed by Direct Numerical Simulations (DNS) to compute the atmospheric jet stream at the tropopause. The basic state is characterised by a jet centred at the tropopause and stable density stratification profile with increased stratification above the tropopause. Quasi-equilibrium turbulent flow-fields are obtained after long-time integration of the governing equations written in primitive variables using adaptive spectral domain decomposition method. The coherent vortex tubes are extracted from the vorticity and potential vorticity fields, using a nonlinear filtering in wavelet space. It is finally checked that the coherent vortex tubes exhibit the same dynamics as the total flow and therefore drive the residual background flow.