Relevance. Turbulent flows are readily met in a variety of engineering applications. In particular, oil and gas transport through pipelines reaching 12 % of the oil-related power consumption is performed at very high Reynolds numbers, i. e. in the turbulent regime. Control of turbulent flow characteristics is the problem of high importance both from scientific and economical point of view. Rapidly developing computing capabilities make the numerical modeling a promising tool to solve various engineering optimization tasks. The aim of the research. For accurate numerical solution of the Navier-Stokes equations especially at high Reynolds numbers it is necessary to use numerical schemes with low dissipation, i.e. with a high order of approximation. A good method for spatial discretization is the spectral element method (SEM). In the work a canonical turbulent flow in a plane channel is simulated with SEM. The main aim of the research is to investigate the accuracy of SEM when applied to the filtered Navier-Stokes equations closed with the use of the dynamic Smagorinsky model. Methods. For numerical simulations of partial differential equations with SEM the authors have used the open-source code Nek5000 which employs unstructured hexahedral meshes and MPI for parallel computing. Results. The authors carried out the numerical computations of the turbulent channel flow at the Reynolds numbers 2800 and 6800. The results of the direct numerical simulation (DNS) of the Navier-Stokes equations and Large eddy simulations (LES) are in good agreement with the data from the literature, i. e. the profiles of the time-averaged velocity, temperature and their fluctuations. Even for very coarse LES mesh with 25-30 times less grid points than for DNS the accuracy of the fluctuations profile near the wall representing streaky structures is very high. As a result the friction velocity is predicted within the <3,0 % error indicating promising prospects for SEM.