OPTIMAL EXCITATION OF 3-DIMENSIONAL PERTURBATIONS IN VISCOUS CONSTANTSHEAR-FLOW

The three-dimensional perturbations to viscous constant shear flow tha t increase maximally in energy over a chosen time interval are obtaine d by optimizing over the complete set of analytic solutions. These opt imal perturbations are intrinsically three dimensional, of restricted morphology, and exhibit large energy growth on the advective time scal e, despite the absence of exponential normal modal instability in cons tant shear flow. The optimal structures can be interpreted as combinat ions of two fundamental types of motion associated with two distinguis hable growth mechanisms: streamwise vortices growing by advection of m ean streamwise velocity to form streamwise streaks, and upstream tilti ng waves growing by the down gradient Reynolds stress mechanism of two -dimensional shear instability. The optimal excitation over a chosen i nterval of time comprises a combination of these two mechanisms, chara cteristically giving rise to tilted roll vortices with greatly amplifi ed perturbation energy. It is suggested that these disturbances provid e the initial growth leading to transition to turbulence, in addition to providing an explanation for coherent structures in a wide variety of turbulent shear flows.