Wade Schoppa

Coherent structure generation in near-wall turbulence

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 prole 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 buer layer exceed the strength threshold for instability. More importantly, these unstable streaks exhibit only moderate (twofold) normalmode amplication, the growth being arrested by self-annihilation of streak-flank normal vorticity due to viscous cross-diusion. We present here an alternative, streak transient growth (STG) mechanism, capable of producing much larger (tenfold) linear amplication 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 !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 !x sheet’s collapse via stretching by @u=@x (rather than rollup) into streamwise vortices. Signicantly, 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.

A large-scale control strategy for drag reduction in turbulent boundary layers

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 sl...

A new mechanism of small-scale transition in a plane mixing layer : core dynamics of spanwise vortices

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.

Formation of near-wall streamwise vortices by streak instability

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 (ωx 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.

Effective drag reduction by large-scale manipulation of streamwise vortices in near-wall turbulence

Using direct numerical simulations of turbulent channel flow, we present new insight into the regeneration dynamics and control of near-wall longitudinal vortices, which dominate turbulence production, drag, and heat transfer. Initially linear instability of lifted low-speed streaks, free from any initial vortex, is shown to generate these dominant streamwise vortices upon (nonlinear) saturation. 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 caused by the positive du/dx (i.e. positive VISA) associated with streak waviness rather than roll-up of cox sheets. Significantly, the 3D features of the instability-generated vortices are close to those of both instantaneous and ensemble-averaged flows, suggesting that this instability mechanism is prevalent in the (uncontrolled) fully turbulent flow. We develop effective new control approaches for turbulent boundary layers, via large-scale streak manipulation, which exploit this crucial role of streaks in vortex generation and hence turbulence production. Using control flows with no x variation, a spanwise wavelength of 400 wall units, and a (frozen) amplitude of only 5% of the channel centerline velocity, we find a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding spanwise wall jet-like forcing. These results suggest promising new drag reduction strategies, e.g. passive vortex generators and spanwise jets from ^-aligned slots, involving large-scale (hence more durable) actuation and requiring no wall sensors or feedback logic.

Nonlinear Instability of Free Shear Layers: Subharmonic Resonance and Three-Dimensional Vortex Dynamics

The subharmonic resonance phenomenon in a free shear layer is studied experimentally and numerically. Excitation using both fundamental and subharmonic at an initial phase difference (ϕin shows stable pairing for a wide range of ϕin. However, for a narrow range of ϕin, either ‘shredding’ occurs or pairing is temporarily suppressed and occurs downstream without periodicity. Under detuned excitation, which is more representative of feedback-driven subharmonic growth, amplitude and phase modulations produce multiple sideband frequencies reflecting variations in the pairing location and occasional nonpairings. In direct numerical simulations (DNS) of a temporal shear layer, we uncover and analyze a new mechanism of transition, based on excitation of the ‘bulging’ instability by pairing of spanwise vortices (‘rolls’) with out-of-phase spanwise undulations. This 3D pairing generates strong internal core dynamics, consisting of core size oscillation driven by oscillating cells of spanwise flow within the rolls. Core dynamics amplify due to instability, can grow alongside streamwise vortices (‘ribs’), and eventually initiate mixing transition at a lower initial 3D disturbance level than that required for transition by ribroll interaction alone. We emphasize that the limitations of traditional perturbation analysis in understanding of the nonlinear and 3D aspects of instability and transition need to be overcome by new approaches such as vortex dynamics and topology.

Dynamics of Slender Vortices Near the Wall in a Turbulent Boundary Layer

It is now well-established that the enhanced drag and heat transfer of turbulent boundary layers are dominated by slender longitudinal vortices near the wall. Despite their immense practical significance, the geometry and dynamics of near-wall vortices are poorly understood and often controversial. To gain new insight into the near-wall dynamics, we educe coherent structures (CS) from a numerically simulated turbulent channel flow — 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 — a region of negative λ2, the second largest eigenvalue of the tensor S ik S kj + ΩikΩkj — which accurately captures the structure details, unlike velocity, vorticity or pressure-based eduction. Extensive testing shows that λ2 correctly captures vortical structures, even in the presence of strong shear as occurring near the wall of a boundary layer. The CS are elongated quasi-streamwise vortices, inclined 9° in (x,y) and tilted ±4° in (x,z), with vortices of alternating sign overlapping in x as a staggered array. Notably, the often heralded hairpin vortices, not to be confused with hairpin-shaped vortex line bundles, are absent both in the instantaneous and ensemble-averaged fields. Our conceptual model of the CS array reproduces nearly all experimentally observed events reported in the literature, such as VITA/VISA, Reynolds stress distributions (Q1, Q2, Q3 and Q4 and their relative contributions), wall pressure variation, elongated low-speed streaks, spanwise shear, etc. We also develop a new CS regeneration mechanism, in which existing CS leave behind lifted low-speed streaks, whose instability in turn initiates the formation of new streamwise vortices.

Dynamics and Control of Near-Wall Coherent Structures

Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction by prevention of streamwise vortex formation near the wall. Instability of lifted, vortex-free low-speed streaks is shown to generate new streamwise vortices, which dominate near-wall turbulence phenomena. 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. Based on this crucial role of streak instability in vortex generation, we develop a new technique for drag reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, x-independent forcing, with a 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 the underlying streak instability. In particular, the forcing significantly weakens the wall-normal vorticity flanking lifted low-speed streaks, thereby arresting the streaks’ instability responsible for vortex generation. These results suggest promising new drag reduction strategies, e.g. passive vortex generators or colliding spanwise jets from x-aligned slots, involving large-scale (hence more durable) actuation and requiring no wall sensors or control logic.