PROLOGUE

This chapter deals with Reynolds number effects in turbulent shear flows with particular emphasis on the canonical zero-pressure-gradient boundary layer and twodimensional channel-flow problems. The Reynolds numbers encountered in many practical situations are typically several orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds-number research facilities are expensive to build and operate, and the few that exist are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Likewise, full computational simulation of high-Reynolds-number flows is beyond the reach of current capabilities. Understanding turbulence and modeling will therefore continue to play vital roles in the computation of high-Reynolds-number practical flows using the Reynolds-averaged Navier–Stokes equations. Because the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed toward the low Reynolds numbers, the key question in such high-Reynolds-number modeling as well as in devising novel flow control strategies is, What are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Understanding the Reynolds number effects is important for flow control on two counts:

1. A passive or active control device developed in a low-Reynolds-number facility may perform quite differently at high Re.

2. For reactive control, coherent structures are targeted.