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 ωy, 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.
|Number of pages||10|
|State||Published - Sep 25 2000|