Borders of disorder

A quantitative theory is described for the boundary layer of fully turbulen t parallel shear flow. In past literature, this region has been called the "laminar sublayer" and enters as a central amplitude-determining factor int o the current empirical statistical descriptions of the full flow. The idea lization explored here parallels the ingenious view advanced by Howard [1] to interpret the fully developed thermal convective boundary layer. Howard pictured a thermal boundary layer swept away by a swift convective instabil ity, and then reestablishing itself on a diffusive time scale. Here, a para llel study for the shear-flow boundary layer is advanced based on the presu mption that the time-dependent instability of the growing diffusive layer i s a dominant first-order aspect of this essentially nonlinear process. The quantitative results support this ordering, as do the initial nonlinear flo ws emerging from the growing instability. Application of these findings is made to the problem of thermal convection with an external flow, which modi fies the instability. Also studied is the "classical" initial instability o f parallel shearing flow, and from these results, possible improvement in u pper bound theories for turbulent flows.