Scaling of turbulence and turbulent mixing using Terascale numerical simulations

Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers (Rlambda) ranging from 8 to 650 and Schmidt numbers (Sc) from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation.; Simulations up to 20483 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors. Benchmark tests indicate very good parallel performance for resolutions up to 40963 on up to 32768 processors, which is highly promising for future simulations at higher resolutions and processor counts eventually to approach Petascale levels.; Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. However, statistics up to fourth order are satisfactory if the grid spacing is not larger than Komogorov scale, without the requirement of a clear analytic range for corresponding structure functions as suggested by recent theories. Results from highly resolved simulations provide support for a modified resolution criterion derived in this work for structure functions of different orders and as a function of Rlambda. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before. The far tails of the probability density functions of dissipation and enstrophy appear to coincide, suggesting a universal scaling of small scales.; Simulations at Rlambda ≈ 650 on 2048 3 grids with scalars at Sc = 1/8 and 1 have allowed us to obtain the clearest evidence of attainment of k -5/3 inertial-convective scaling in the scalar spectrum (as function of wavenumber k) in numerical simulations to date. In addition, results at high Sc appear to support k -1 viscous-convective scaling. Intermittency for scalars as measured by the tail of the PDF of scalar dissipation and moments of scalar gradient fluctuations is found to saturate at high Sc. This asymptotic state is reached at lower Sc when R lambda is high. Statistics of scalar gradients in different directions are used to address the scaling of anisotropy due to the imposed mean scalar gradient. Persistent departures from isotropy are observed as R lambda increases. However, results suggest a return to isotropy at high Schmidt numbers, a tendency that appears to be stronger at high Reynolds numbers.; The effects of the Coriolis force on turbulence under solid-body rotation are investigated using simulations at 10243 resolution on enlarged solution domains which reduce the effects of periodic boundary conditions due to the growth of integral scales. Anisotropy at all scales is observed, and is strongest at intermediate rotation rates. Spectra, structure functions and different alignments show strong departures from classical scaling. At high rotation rates the nonlinear terms are damped which help explain the observed decrease in intermittency. The basic property of enstrophy production through vortex stretching in non-rotating flows is also reduced at high rotation rates. Results from DNS do not appear to support some of the assumptions leading to the classical form of the Taylor-Proudman theorem. A mechanism for mixing and a scaling for structure functions is proposed for rapidly rotating flows.