Accelerated computing that uses graphics processing unit (GPU) technology has become very popular and nine out of the top ten systems in the Top 500 list use such accelerators. Many approaches strive to make software development for these systems easier and more portable. The OpenMP application programming interface (API) enables portable access to GPU-accelerated computing for C/C++ and Fortran at high productivity. In this paper, we evaluate the performance of the most important compute kernels of the Fortran application STREAmS for computational fluid dynamics (CFD) problems. Our experiments show that the AMD Next-Gen Fortran Compiler achieves more than 85% of the performance of the manually tuned kernels written using the HIP API. This makes the OpenMP API an attractive choice for high-productivity access to accelerated computing for Fortran applications.