It is a truism that turbulence is an unsolved problem, whether in scientific, engin eering or geophysical terms. It is strange that this remains largely the case even though we now know how to solve directly, with the help of sufficiently large and powerful computers, accurate approximations to the equations that govern tur bulent flows. The problem lies not with our numerical approximations but with the size of the computational task and the complexity of the solutions we gen erate, which match the complexity of real turbulence precisely in so far as the computations mimic the real flows....

Progress in the numerical simulation of turbulence has been rapid in the 1990s. New techniques both for the numerical approximation of the Navier-Stokes equations and for the subgrid-scale models used in large-eddy simulation have emerged and are being widely applied for both fundamental and applied engineering studies, along with ideas for the performance and use of simulation for compressible, chemically reacting and transitional flows.

It is a truism that turbulence is an unsolved problem, whether in scientific, engin- eering or geophysical terms. It is strange that this remains largely the case even though we now know how to solve directly, with the help of sufficiently large and powerful computers, accurate approximations to the equations that govern tur- bulent flows. The problem lies not with our numerical approximations but with the size of the computational task and the complexity of the solutions we gen- erate, which match the complexity of real turbulence precisely in so far as the computations mimic the real flows....