Generation of near-wall coherent structures in a turbulent boundary layer

Using direct numerical simulations of turbulent channel flow, we present new insight into the generation of streamwise vortices near the wall, and an associated drag reduction strategy. Growth of x-dependent spanwise velocity disturbances w(x) is shown to occur via two mechanisms: (i) linear transient growth, which dominates early-time evolution, and (ii) linear normal-mode instability, dominant asymptotically at late time (for frozen base flow streaks). Approximately 25% of streaks extracted from near-wall turbulence are shown to be strong enough for linear instability (above a critical vortex line lift angle). However, due to viscous annihilation of streak normal vorticity ω_y, normal mode growth ceases after a factor of two energy growth. In contrast, the linear transient disturbance produces a 2-fold amplification, due to its rapid, early-time growth before significant viscous streak decay. Thus, linear transient growth of w(x) is revealed as a new, apparently dominant, generation mechanism of x-dependent turbulent energy near the wall. Combined transient growth/instability of lifted, . vortex-free low-speed streaks (above the instability cutoff of streak strength) is shown to generate new streamwise vortices, which dominate near-wall turbulence phenomena. This new vortex formation mechanism consists of: (i) streak waviness in the horizontal plane caused by w(x) disturbance growth, (ii) generation of horizontal sheets of streamwise vorticity and induction of positive stretching ∂u/∂x (i.e. positive VISA), inherent to streak waviness, and finally (iii) vorticity sheet collapse via stretching (rather than roll-up) into streamwise vortices. Significantly, the 3D features of the (instantaneous) vortices generated by transient/instability growth agree well with the coherent structures educed (i.e. ensemble-averaged) from fully turbulent flow, suggesting the prevalence of this mechanism. Results suggest promising new strategies for drag and heat transfer control, involving large-scale (hence more durable) actuators, without requiring wall sensors or control logic.