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Direct Numerical Simulations (DNS) of the Navier Stokes equations is aninvaluable research tool in fluid dynamics. Still, there are few publiclyavailable research codes and, due to the heavy number crunching implied,available codes are usually written in low-level languages such as C/C++ orFortran. In this paper we describe a pure scientific Python pseudo-spectral DNScode that nearly matches the performance of C++ for thousands of processors andbillions of unknowns. We also describe a version optimized through Cython, thatis found to match the speed of C++. The solvers are written from scratch inPython, both the mesh, the MPI domain decomposition, and the temporalintegrators. The solvers have been verified and benchmarked on the Shaheensupercomputer at the KAUST supercomputing laboratory, and we are able to showvery good scaling up to several thousand cores.  A very important part of the implementation is the mesh decomposition (weimplement both slab and pencil decompositions) and 3D parallel Fast FourierTransforms (FFT). The mesh decomposition and FFT routines have been implementedin Python using serial FFT routines (either NumPy, pyFFTW or any other serialFFT module), NumPy array manipulations and with MPI communications handled byMPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFTin Python for a slab mesh decomposition using 4 lines of compact Python code,for which the parallel performance on Shaheen is found to be slightly betterthan similar routines provided through the FFTW library. For a pencil meshdecomposition 7 lines of code is required to execute a transform.

High performance Python for direct numerical simulations of turbulent flows