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Coherent structures near the wall in a turbulent channel flow

Published online by Cambridge University Press:  10 February 1997

J. Jeong ,
F. Hussain ,
W. Schoppa  and
J. Kim
J. Jeong
Affiliation:
, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, USA
F. Hussain
Affiliation:
, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, USA
W. Schoppa
Affiliation:
, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, USA
J. Kim
Affiliation:
, Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095-1597, USA
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 185 - 214
Copyright
Copyright © Cambridge University Press 1997

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