The mean streak spacing of approximately 100 wall units that is observed in wall-bounded turbulent shear flow is shown to be consistent with near-wall streamwise vortices optimally configured to gain the most energy over an appropriate turbulent eddy turnover time. The streak spacing arising from the optimal perturbation increases with distance from the wall and is nearly independent of Reynolds number, in agreement with experiment.

A well-established characteristic of wall-bounded turbulent shear flow is the presence near the wall of regions of high-and low-speed fluid that are elongated in the streamwise direction and alternate in the spanwise direction. These streaky structures are observed to play an important role in the maintenance of turbulence through the “bursting” process, which is responsible for most of the turbulent kinetic energy production in the boundary layer.‘?’The observed mean spanwise spacing between lowspeed streaks is consistently found to be AZ,: 100 wall units. The superscript+ indicates quantities scaled by wall variables, according to which distance and time are nondimensionalized as y’=-vu/v and t+= tuyv, where v is the kinematic viscosity and u7=[v (dU/dy) 1 w] ln is the friction velocity, the subscript w denoting a value at the wall. The distribution of streak spacings is broad, with the coefficient of variation &= az/; l+ Z~~ 0.30-0.40, where of is the standard deviation. 3 The mean streak spacing is observed to increase with distance from the wa11, 3V4 and is essentially independent of Reynolds number. 3 It is generally accepted that the streak formation mechanism is linear and arises from the redistribution of mean momentum by streamwise rolls. This is evident, for example, in the comparison by Lee et al.’of turbulent fields resulting from direct numerical simulation (DNS) to those developed using the linearized equations of rapid distortion theory (RDT) from the same initially isotropic turbulent field. It is reasonable, therefore, to ask whether the scale selection responsible for the observed streak spacing also arises from linear theory. An attempt by Waleffe and Kim6 to obtain the characteristic scale using the linear theories of selective amplification’and direct resonance* was unsuccessful, leading them to propose that the selection mechanism must be nonlinear and self-sustaining. In &is work, we use optimal perturbation theory to show that the lOO+ streak spacing is consistent with linear growth limited by turbulent disruption. Optimal perturbation theory seeks the linear perturbations in a given background flow that grow by the largest amount in a chosen norm over a specified period of time. Mathematical details are presented in full in a recent paper. g In brief, an arbitrary three-dimensional disturbance that is periodic in the spanwise z and streamwise x directions can be represented as a sum of eigenmodes