Direct numerical simulation (DNS) for incompressible turbulent channel flow at Reτ = 5200

Nearly all moving objects on Earth pass through fluids and many of them move at high speed. This makes high Re wall-bounded turbulent flows of great technological impor- tance. To study high Re wall-bounded turbulence, high spatial and temporal resolution is required due to the multi-scale nature of turbulence. Direct numerical simulation (DNS) is a technique for the study of turbulence in which the Navier-Stoke equations, the governing equations of fluid flow, are solved with sufficient resolution to represent all the scales of tur- bulence. Hence, DNS is very expensive and always limited by computational capability. To perform DNS on the most advanced high performance computing systems, extensive code optimization is required. A new turbulence DNS code, PoongBack, was developed for the studies reported here. It shows excellent performance and scalability (∼97%) on upto 786k cores on Mira at Argonne Leadership Computing Facility.

We have performed DNS of turbulent channel flow using a Fourier-Galerkin method in the streamwise(x) and spanwise (z) directions and a B-Splines collocation method in the wall-normal (y) direction. The highest Reynolds number based on shear velocity (uτ = √(τw/ρ)), Reτ is approximately 5200. The simulation results exhibit a number of the char- acteristics of high Re wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant κ = 0.384±0.004. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits 1/k dependence over a short range in wavenum- ber (k). Further, consistent with previous experimental observations, when these spectra are multiplied by k (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the 1/k range.

To study the scale dependence of the dynamics of the Reynolds stress components, we applied a spectral analysis to the terms in the Reynolds stress transport equation (RSTE). It is shown that only the turbulent transport terms show significant Re dependencies. Further- more, the turbulent transport terms can be decomposed into two parts, one that contributes to transport in the wall-normal direction and one that is responsible for transfer between length scales. The results show that the large scale motion in the outer region has direct effects on the flow in the near-wall region through transport of turbulent kinetic energy. Also, a reverse energy cascade from intermediate scales to large scales is observed in the spanwise velocity fluctuations.