We present a new mechanism for generation of near-wall streamwise vortices -which dominate turbulence phenomena in boundary layers -using linear perturbation analysis and direct numerical simulations of turbulent channel flow. The base flow, consisting of the mean velocity profile and low-speed streaks (free from any initial vortices), is shown to be linearly unstable to sinuous normal modes only for relatively strong streaks, i.e. for wall inclination angles of streak vortex lines exceeding 50• . Analysis of streaks extracted from fully developed near-wall turbulence indicates that about 20% of streak regions in the buffer layer exceed the strength threshold for instability. More importantly, these unstable streaks exhibit only moderate (twofold) normalmode amplification, the growth being arrested by self-annihilation of streak-flank normal vorticity due to viscous cross-diffusion. We present here an alternative, streak transient growth (STG) mechanism, capable of producing much larger (tenfold) linear amplification of x-dependent disturbances. Note the distinction of STG -responsible for perturbation growth on a streak velocity distribution U(y, z) -from prior transient growth analyses of the (streakless) mean velocity U(y). We reveal that streamwise vortices are generated from the more numerous normal-mode-stable streaks, via a new STG-based scenario: (i) transient growth of perturbations leading to formation of a sheet of streamwise vorticity ω x (by a 'shearing' mechanism of vorticity generation), (ii) growth of sinuous streak waviness and hence ∂u/∂x as STG reaches nonlinear amplitude, and (iii) the ω x sheet's collapse via stretching by ∂u/∂x (rather than rollup) into streamwise vortices. Significantly, the three-dimensional features of the (instantaneous) streamwise vortices of x-alternating sign generated by STG agree well with the (ensemble-averaged) coherent structures educed from fully turbulent flow. The STGinduced formation of internal shear layers, along with quadrant Reynolds stresses and other turbulence measures, also agree well with fully developed turbulence. Results indicate the prominent -possibly dominant -role of this new, transient-growth-based vortex generation scenario, and suggest interesting possibilities for robust control of drag and heat transfer.

Coherent structures (CS) near the wall (i.e. y + ≤ 60) in a numerically simulated turbulent channel flow are educed using a conditional sampling scheme which extracts the entire extent of dominant vortical structures. Such structures are detected from the instantaneous flow field using our newly developed vortex definition (Jeong & Hussain 1995) - a region of negative λ2, the second largest eigenvalue of the tensor SikSkj + ΩikΩkj - which accurately captures the structure details (unlike velocity-, vorticity- or pressure-based eduction). Extensive testing has shown that λ2 correctly captures vortical structures, even in the presence of the strong shear occurring near the wall of a boundary layer. We have shown that the dominant near-wall educed (i.e. ensemble averaged after proper alignment) CS are highly elongated quasi-streamwise vortices; the CS are inclined 9° in the vertical (x, y)-plane and tilted ±4° in the horizontal (x, z)-plane. The vortices of alternating sign overlap in x as a staggered array; there is no indication near the wall of hairpin vortices, not only in the educed data but also in instantaneous fields. Our model of the CS array reproduces nearly all experimentally observed events reported in the literature, such as VITA, Reynolds stress distribution, wall pressure variation, elongated low-speed streaks, spanwise shear, etc. In particular, a phase difference (in space) between streamwise and normal velocity fluctuations created by CS advection causes Q4 ('sweep’) events to dominate Q2 ('ejection’) and also creates counter-gradient Reynolds stresses (such as Ql and Q3 events) above and below the CS. We also show that these effects are adequately modelled by half of a Batchelor's dipole embedded in (and decoupled from) a background shear U(y). The CS tilting (in the (x, z)-plane) is found to be responsible for sustaining CS through redistribution of streamwise turbulent kinetic energy to normal and spanwise components via coherent pressure-strain effects.

Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, x-independent forcing, with a z wavelength of 400 wall units and an amplitude of only 6% of the centerline velocity, produces a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding, z-directed wall jets. The drag reduction results from weakened longitudinal vortices near the wall, due to forcing-induced suppression of an underlying streak instability mechanism. In particular, the forcing significantly weakens the wall-normal vorticity ωy flanking lifted low-speed streaks, thereby arresting the streaks’ sinuous instability which directly generates new streamwise vortices in uncontrolled flows. These results suggest promising new drag reduction techniques, e.g., passive vortex generators or colliding spanwise jets from x-aligned slots, involving durable actuators and no wall sensors or control logic.

The regeneration and dynamics of near-wall longitudinal vortices -which dominate turbulence production, drag, and heat transfer -are analyzed using direct numerical simulation of turbulent channel ow. These dominant streamwise vortices are shown to result from nonlinear saturation of an instability of lifted low-speed streaks near a single wall, free from any initial vortex. The newly-found instability mechanism initiates streak waviness in the (x; z) plane, generating streamwise vorticity sheets. Streak waviness in turn induces positive @u=@x (i.e. positive VISA), which causes these sheets' vorticity to then concentrate via stretching (rather than roll up) into new streamwise vortices. The instability requires su ciently strong streaks (y circulation per unit x ¿ 7:6 wall units) and is inviscid in nature, despite the close proximity of the no-slip wall. We ÿnd that self-annihilation of streaks due to viscous cross-di usion of opposite-signed wall normal vorticity across each streak causes the instability ampliÿcation to scale in wall units, suggesting the relevance of our results to high Re as well. Signiÿcantly, the strongly 3D vortices generated by streak instability agree well with the CS educed from fully turbulent ow, suggesting the prevalence of this streak instability-based vortex formation mechanism. Simultaneous to vortex generation, an internal shear layer is generated across the streak from each streamwise vortex by stretching of spanwise vorticity. Such a shear layer eventually rolls up at the downstream end of a streamwise vortex, and the two link up and propagate outward to form a spanwise "arch" vortex. The newly generated streamwise vortices act to sustain=strengthen the preexisting streak which spawned them through localized lifting of near-wall uid by induction. We develop a new spatiotemporal vortex generation mechanism, in which vortices leave behind "vortex-less" streaks, whose instability, due to the mechanism explained herein, initiates streamwise vortex formation.

We present a new mechanism of small-scale transition via core dynamics instability (CDI) in an incompressible plane mixing layer, a transition which is not reliant on the presence of longitudinal vortices (‘ribs’) and which can originate much earlier than ribinduced transition. Both linear stability analysis and direct numerical simulation are used to describe CDI growth and subsequent transition in terms of vortex dynamics and vortex line topology. CDI is characterized by amplifying oscillations of core size non-uniformity and meridional flow within spanwise vortices (‘rolls’), produced by a coupling of roll swirl and meridional flow that is manifested by helical twisting and untwisting of roll vortex lines. We find that energetic CDI is excited by subharmonic oblique modes of shear layer instability after roll pairing, when adjacent rolls with out-of-phase undulations merge. Starting from moderate initial disturbance amplitudes, twisting of roll vortex lines generates within the paired roll opposing spanwise flows which even exceed the free-stream velocity. These flows collide to form a nearly irrotational bubble surrounded by a thin vorticity sheath of a large diameter, accompanied by folding and reconnection of roll vortex lines and local transition. We find that accelerated energy transfer to high wavenumbers precedes the development of roll internal intermittency; this transfer, inferred from increased energy at high wavenumbers and an intensification of roll vorticity, occurs prior to the development of strong opposite-signed (to the mean) spanwise vorticity and granularity of the roll vorticity distribution. We demonstrate that these core dynamics are not reliant upon special symmetries and also occur in the presence of moderate-strength ribs, despite entrapment of ribs within pairing rolls. In fact, the roll vorticity dynamics are dominated by CDI if ribs are not sufficiently strong to first initiate transition; thus CDI may govern small-scale transition for moderate initial 3D disturbances, typical of practical situations. Results suggest that CDI constitutes a new generic mechanism for transition to turbulence in shear flows.

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