Some contributions and challenges of computational turbulence research

The contributions of numerical simulations to the changes that have taken place during the past twenty years in our understanding of near-wall turbulence, and of the dissipative scales of isotropic flows, are briefly reviewed. It is argued that both problems have moved over this time from empirical observations to relatively coherent theoretical models, and that much of the reason is that they could be simulated cheaply enough to subject them to conceptual experiments. This required a lapse of ten to fifteen years after they were first computed, over which time the cost of simulations decreased by a factor of 100. Simulations of the logarithmic layer and of the inertial energy cascade and now beginning to be affordable. Both are still too expensive to experiment with them, but it is argued that, if history can be taken as a guide, both problems will become routinely computable in the next decade, and that we will then be able to attack their dynamics.