The interaction between inner and outer regions of turbulent wall-bounded flow

The nature of the interaction between the inner and outer regions of turbulent wall-bounded flow is examined. Townsend's theory of inactive motion is shown to be a first-order, linear approximation of the effect of the large eddies at the surface that acts as a quasi-inviscid, low-frequency modulation of the shear-stress-bearing motion. This is shown to be a ‘strong’ asymptotic condition that directly expresses the decoupling of the inner-scale active motion from the outer-scale inactive motion. It is further shown that such a decoupling of the inner and outer vorticity fields near the wall is inappropriate, even at high Reynolds numbers, and that a ‘weak’ asymptotic condition is required to represent the increasing effect of outer-scale influences as the Reynolds number increases. High Reynolds number data from a fully developed pipe flow and the atmospheric surface layer are used to show that the large-scale motion penetrates to the wall, the inner–outer interaction is not describable as a linear process and the interaction should more generally be accepted as an intrinsically nonlinear one.