3 results
A new mechanism of small-scale transition in a plane mixing layer: core dynamics of spanwise vortices
- W. Schoppa, F. Hussain, R. W. Metcalfe
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- Journal:
- Journal of Fluid Mechanics / Volume 298 / 10 September 1995
- Published online by Cambridge University Press:
- 26 April 2006, pp. 23-80
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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.
Coherent structure generation in near-wall turbulence
- W. SCHOPPA, F. HUSSAIN
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- Journal:
- Journal of Fluid Mechanics / Volume 453 / 25 February 2002
- Published online by Cambridge University Press:
- 06 March 2002, pp. 57-108
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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) normal-mode 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 ampliflcation 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 ωx (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 ωx 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 STG-induced 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 near the wall in a turbulent channel flow
- J. Jeong, F. Hussain, W. Schoppa, J. Kim
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- Journal:
- Journal of Fluid Mechanics / Volume 332 / February 1997
- Published online by Cambridge University Press:
- 10 February 1997, pp. 185-214
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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.