Abstract
Perhaps the most distinguishing characteristic of high Reynolds number turbulent flows is their large range of excited space and time scales. In homogeneous turbulence, dissipation-scale eddies are of order R3/4 times smaller than energy-containing eddies, where R is the Reynolds number. In order to solve the Navier-Stokes equations accurately for such a turbulent flow, it is necessary to retain order (R3/4)3 spatial degrees of freedom. Also, since the time scale for significant evolution of homogeneous turbulence is of the order of the turnover time of an energy containing eddy, it is necessary to perform order R3/4 time steps to calculate for a significant evolution time of the flow. Even if these calculations require only O(1) arithmetic operations per degree of freedom per time step, the total computational work involved would be order R3, while the computer storage requirement would be R9/4. In this case, doubling the Reynolds number would require an order of magnitude improvement in computer capability. With this kind of operation and storage count, it is unlikely that forseeable advances in computers will allow the full numerical simulation of turbulent flows at Reynolds numbers much larger than Rλ = 0(100) already achieved (see BRACHET et al. [2]).
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