The conceptual analysis of turbulent flow and convection

The complexity and intractability of the mathematical description of turbulent flow forced early investigators to utilize conceptual analysis of various types. The accumulative results of such analyses by the giants of our field over the past century are shown in retrospect to provide a complete and essentially exact structure for the correlation of experimental data and recent results from direct numerical simulations. This approach is found to be less successful for turbulent convection because of its greater intrinsic complexity but the limited integral formulations for specific values of the Prandtl number do provide invaluable theoretical guideposts.