Is There an Asymptotic Effect of Initial and Upstream Conditions on Turbulence?

Abstract

More than two decades ago the first strong experimental results appeared suggesting that turbulent flows might not be asymptotically independent of their initial (or upstream) conditions [1]. And shortly thereafter the first theoretical explanations were offered as to why we came to believe something about turbulence that might not be true [2]. It was recognized immediately that if turbulence was indeed asymptotically independent of its initial conditions, it meant that there could be no universal single point model for turbulence [2], [3], certainly consistent with experience, but not easy to accept for the turbulence community. Even now the ideas of asymptotic independence still dominate most texts and teaching of turbulence. This paper reviews the substantial additional evidence — experimental, numerical and theoretical — for the asymptotic effect of initial and upstream conditions that has accumulated over the past 20 years. Emphasis has been placed on the canonical turbulent flows (especially wakes, jets, and homogeneous decaying turbulence), which have been the traditional building blocks for our understanding. Some of the implications for the future of turbulence modeling and research, especially LES and turbulence control, are also considered.