Role of Initial Conditions in Establishing Asymptotic Flow Behavior

The role of the details of initial (or upstream) conditions in establishing asymptotic behavior is reviewed. The traditional view that at least simple shear flows reach universal asymptotic states is shown to be inconsistent with the abundant experimental and direct-numerical-simulation data. Even though scaled mean velocity profiles collapse, the streamwise (or temporal) variation of the scaling parameters and spreading rates can vary widely for different upstream (or initial) conditions. Equilibrium similarity theory shows why the traditional view has arisen: normalized mean velocity profiles can be universal, even though the other moment profiles and scaling parameters are not. Decaying isotropic turbulence and applications of the proper orthogonal decomposition to free shear flows are used to show what parameters might control the downstream development. It is argued that Reynolds-averaged Navier-Stokes cannot account for these dependencies, but large-eddy simulation can.