ABSTRACT
A dimensional analysis based on one-scale for each variable leads to an implicit relation among dimensionless numbers. In contrast, a dimensional analysis based on multi-scales for at least one variable leads to an explicit relation among dimensionless numbers. This chapter concerns multi-scale dimensional analysis of turbulent flows. Before getting involved with the complexity of these flows, it illustrates the foundations of multi-scale dimensional analyses in terms of a couple examples involving laminar flows. Foregoing considerations suggest that the scales for fluctuations should be different from those for the mean flow. Accordingly, we may construct a turbulence model to be based on two sets of scales, one set for the mean flow and one set for fluctuations. The dissipation may be interpreted as a passive process proceeding at a rate dictated by the inviscid inertial behavior of large eddies.
