The spectral method provides an efficient algorithm for solving the three dimensional incompressible Navier–Stokes equations in periodic boundaries. Most people, so far, have used vectorized machines, such as the CRAY‐2, to implement fast Fourier transformations and time integrations in the spectral calculations. In this paper, new results are presented using the spectral calculations on the Connection Machine‐2 with a parallel algorithm. The large memory of the Connection Machine‐2 and the parallel algorithm allows one, for the first time, to implement a 5123 mesh resolution for high Reynolds number flows. The computational speed of the present code is about 30% faster than the fastest CRAY‐2 simulations with four processors. Parallel machines, such as the Connection Machine‐2, will possibly provide new computational power for understanding the intermittency and cascade mechanism in fluid turbulence.

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