High-resolution direct numerical simulation of turbulence

We performed high-resolution direct numerical simulations (DNS) of incompressible turbulence in a periodic box by using a Fourier spectral method with the number of grid points up to 4096(3). The simulations consist of two series: one with k(max)eta similar to 1 ( series 1), and the other with k(max)eta similar to 2 (series 2), where k(max) is the highest wavenumber in each simulation, and. is the Kolmogorov length scale. In the 4096(3) DNS, the Taylor scale Reynolds number R-lambda similar to 1200 and the ratio of L/eta of the integral length scale L to eta is approximately 2200, in series 1. The DNS data analysis reveals simple scaling of various spectra, and also sheds some light on (i) the energy spectrum at high R-lambda, (ii) the asymptotic R-lambda-dependence of the normalized energy dissipation rate, (iii) the anomalous scaling of the spectra of energy dissipation and enstrophy, and so on. After some preliminary remarks on the methods and limitations of the DNS, this paper presents a review of the DNS data analysis. Discussions are also made on some questions invoked by the DNS.