Time averaging in turbulence settings may reveal an infinite hierarchy of length scales

Abstract

The problem of discerning key features of steady turbulent flow adjacent to a wall has drawn the attention of some of the most noted fluid dynamicists of all time. Standard examples of such features are found in the mean velocity profiles of turbulent flow in channels, pipes or boundary layers. The aim of this article is to explain and further develop the recent concept of scaling patch for the time-averaged equations of motion of incompressible flow made highly turbulent by friction at a fixed boundary (introduced in recent papers by Wei et al, Fife et al, and Klewicki et al.) Besides outlining ways to identify the patches, which provide the scaling structure of mean profiles, a critical co..