▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

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DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

The organization of vortex clusters above the buffer layer of turbulent channels is analysed using direct numerical simulations at friction Reynolds numbers up to Re τ = 1900. Especial attention is paid to a family of clusters that reach from the logarithmic layer to the near-wall region below y + = 20. These tall attached clusters are markers of structures of the turbulent fluctuating velocity that are more intense than their background. Their lengths and widths are proportional to their heights Ay and grow self-similarly with time after originating at different wall-normal positions in the logarithmic layer. Their influence on the outer region is measured by the variation of their volume density with Δ y . That influence depends on the vortex identification threshold, and becomes independent of the Reynolds number if the threshold is low enough. The clusters are parts of larger structures of the streamwise velocity fluctuations whose average geometry is consistent with a cone tangent to the wall along the streamwise axis. They form groups of a few members within each cone, with the larger individuals in front of the smaller ones. This behaviour is explained considering that the streamwise velocity cones are 'wakes' left behind by the clusters, while the clusters themselves are triggered by the wakes left by yet larger clusters in front of them. The whole process repeats self-similarly in a disorganized version of the vortex-streak regeneration cycle of the buffer layer, in which the clusters and the wakes spread linearly under the effect of the background turbulence. These results characterize for the first time the structural organization of the self-similar range of the turbulent logarithmic region.

Self-similar vortex clusters in the turbulent logarithmic region

Direct numerical simulation (DNS) of a fully developed turbulent channel flow for various Reynolds numbers has been carried out to investigate the Reynolds number dependence. The Reynolds number is set to be Re τ = 180, 395, and 640, where Re τ is the Reynolds number based on the friction velocity and the channel half width. The computation has been executed with the use of the finite difference method. Various turbulence statistics such as turbulence intensities, vorticity fluctuations, Reynolds stresses, their budget terms, two-point correlation coefficients, and energy spectra are obtained and discussed. The present results are compared with the ones of the DNSs for the turbulent boundary layer and the plane turbulent Poiseuille flow and the experiments for the channel flow. The closure models are also tested using the present results for the dissipation rate of the Reynolds normal stresses. In addition, the instantaneous flow field is visualized in order to examine the Reynolds number dependence for the quasi-coherent structures such as the vortices and streaks

Direct Numerical Simulation of a Fully Developed Turbulent Channel Flow With Respect to the Reynolds Number Dependence

Over Arctic sea ice, pressure ridges and floe and melt pond edges all introduce discrete obstructions to the flow of air or water past the ice and are a source of form drag. In current climate models form drag is only accounted for by tuning the air–ice and ice–ocean drag coefficients, that is, by effectively altering the roughness length in a surface drag parameterization. The existing approach of the skin drag parameter tuning is poorly constrained by observations and fails to describe correctly the physics associated with the air–ice and ocean–ice drag. Here, the authors combine recent theoretical developments to deduce the total neutral form drag coefficients from properties of the ice cover such as ice concentration, vertical extent and area of the ridges, freeboard and floe draft, and the size of floes and melt ponds. The drag coefficients are incorporated into the Los Alamos Sea Ice Model (CICE) and show the influence of the new drag parameterization on the motion and state of the ice cover, with the most noticeable being a depletion of sea ice over the west boundary of the Arctic Ocean and over the Beaufort Sea. The new parameterization allows the drag coefficients to be coupled to the sea ice state and therefore to evolve spatially and temporally. It is found that the range of values predicted for the drag coefficients agree with the range of values measured in several regions of the Arctic. Finally, the implications of the new form drag formulation for the spinup or spindown of the Arctic Ocean are discussed.

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Impact of Variable Atmospheric and Oceanic Form Drag on Simulations of Arctic Sea Ice

Large eddy simulation (LES) of the ocean mixed layer was performed in which both wave breaking and Langmuir circulation are realized. Wave breaking was represented by random forcing consistent with the observed near-surface turbulence, and Langmuir circulation was realized by the Craig–Leibovich vortex force. High- resolution simulations were carried out using parallel computing with or without each contribution, wave breaking and Langmuir circulation, with an aim to clarify their respective roles in the ocean mixed layer. The effects of wave breaking were found to be mainly limited to the near-surface zone of the upper few meters. Langmuir circulations below it are not significantly modified, although they become somewhat weakened and less coherent. Under the influence of wave breaking, however, the turbulence production in the upper-ocean mixed layer becomes dominated by the turbulent kinetic energy flux, contrary to the case of the atmospheric boundary layer where it is dominated by shear prod...

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Large Eddy Simulation of the Ocean Mixed Layer: The Effects of Wave Breaking and Langmuir Circulation

乱流予混合火炎のDirect Numerical Simulation

Coherent Fine Scale Eddies and Large-Scale Structures in Wall Turbulence

混合層のダイレクト・シミュレーション : スパン方向じょう乱の影響

Current state and perspective of DNS of turbulence and turbulent combustion are discussed with feature trend of the fastest supercomputer in the world. Based on the perspective of DNS of turbulent combustion, possibility of perfect simulations of IC engine is shown. In 2020, the perfect simulation will be realized with 30 billion grid points by 1EXAFlops supercomputer, which requires 4 months CPU time. The CPU time will be reduced to about 4 days if several developments were achieved in the current fundamental researches. To shorten CPU time required for DNS of turbulent combustion, two numerical methods are introduced to full-explicit full-compressible DNS code. One is compact finite difference filter to reduce spatial resolution requirements and numerical oscillations in small scales, and another is well-known point-implicit scheme to avoid quite small time integration of the order of nanosecond for fully explicit DNS. Availability and accuracy of these numerical methods have been confirmed carefully for auto-ignition, planar laminar flame and turbulent premixed flames. To realize DNS of IC engine with realistic kinetic mechanism, several DNS of elemental combustion process in IC engines has been conducted.

護店橋

Papers

乱流予混合火炎のDirect Numerical Simulation

Coherent Fine Scale Eddies and Large-Scale Structures in Wall Turbulence

混合層のダイレクト・シミュレーション : スパン方向じょう乱の影響

Huge Direct Numerical Simulation of Turbulent Combustion - Toward Perfect Simulation of IC Engine -

MHD一様乱流の非等方化機構 : 第3報,Coherent微細渦による変動磁場形成(流体工学,流体機械)

護 店橋

Papers

乱流予混合火炎のDirect Numerical Simulation

Coherent Fine Scale Eddies and Large-Scale Structures in Wall Turbulence

混合層のダイレクト・シミュレーション : スパン方向じょう乱の影響

Huge Direct Numerical Simulation of Turbulent Combustion - Toward Perfect Simulation of IC Engine -

MHD一様乱流の非等方化機構 : 第3報,Coherent微細渦による変動磁場形成(流体工学,流体機械)

護店橋