Contribution of direct numerical simulation to understanding and modelling turbulent transport

With the advances in large scale computers, reliable numerical methods and efficient post-processing environment, direct numerical simulation (DNS) has become a valuable and indispensable resource for fundamental turbulence research, although DNS is possible only when the turbulent Reynolds (or Peclet) number remains small to moderate. This paper reviews the contribution that various DNSS have made to understanding and modelling turbulent transport phenomena. After general remarks are made on the grid requirements and numerical methods of DNS, its novelties as a numerical experiment are summarized and some of them are demonstrated by introducing typical DNS results at the University of Tokyo. Emphasis is laid upon new findings on the turbulence statistics, their budgets and quasi-coherent eddy structures revealed by the simulations of the fully developed channel flow with heat transport at different Prandtl numbers, and also a recent modelling attempt to take into account the new knowledge extracted from these DNSS, i. e. a remarkable change of the destruction mechanism of turbulent scalar flux with the Prandtl number and a low Reynolds number effect on the redistribution process of the Reynolds stress.