Analysis of a Scale-Similarity Model of the Motion of Large Eddies in Turbulent Flows

Abstract

In turbulent flow, the normal procedure has been to seek means ū of the fluid velocity u rather than the velocity itself. If these means are defined by local spacial averaging with an averaging radius of δ the approach is known as large eddy simulation, and ū denotes the eddies of size 0(δ) and larger. One approach to the closure problem which arises from averaging the nonlinear term is use of a scale-similarity hypothesis. We consider one such scale-similarity model. For this model we show the solution w to the model for ū converging to u as the averaging radius δ→0. We also show that the error ‖ū−w‖ is bounded by the modeling error (perhaps better termed “modeling residual”), evaluated on the true solution u. This last bound suggests one path to validating the model in either computational or physical experiments.