Formation of Near-Wall Streamwise Vortices by Streak Instability

Abstract

Using direct numerical simulations of turbulent channel flow, we present new insight into the formation mechanism of near-wall longitudinal vortices. Instability of lifted, vortex-free low-speed streaks is shown to generate, upon nonlinear saturation, new streamwise vortices, which dominate near-wall turbulence production, drag, and heat transfer. The instability requires sufficiently strong streaks (y circulation per unit x > 7.6) and is inviscid in nature, despite the proximity of the no-slip wall. Streamwise vortex formation (collapse) is dominated by stretching, rather than rollup, of instability generated (ω_x sheets. In turn, direct stretching results from the positive ∂u/∂x (i.e. positive VISA) associated with streak waviness in the (x,z) plane, generated upon finite-amplitude evolution of the sinuous instability mode. Significantly, the 3D features of the (instantaneous) instability-generated vortices agree well with the coherent structures educed (i.e. ensemble averaged) from fully turbulent flow, suggesting the prevalence of this instability mechanism. Fundamental differences in the regeneration dynamics of minimal channel and Couette flows are revealed regarding (nonlinear) streak instability, vortex formation and evolution, and wall shear behavior.