Computing high-Reynolds-number turbulence: will simulations ever replace experiments?

The cost and future prospects of direct and large-eddy numerical simulations are discussed in the context of their use in the development of turbulence theory. It is concluded that even today simulations are comparable to experiments in many aspects, including the Reynolds number, and that simulations at asymptotically large Reynolds numbers should become available within the next decade. For isotropic or free-shear turbulent flows, this should be equivalent to an infinitely large Reynolds number, but to achieve the same result in wall-bounded flows requires the development of a theory for the structure of the logarithmic layer. This is the key obstacle for practical large-eddy simulations of wall flows, and it is argued that its development would be better supported by numerical simulations than by experiments.