TY - JOUR
T1 - Coherent structures near the wall in a turbulent channel flow
AU - Jeong, J.
AU - Hussain, F.
AU - Schoppa, W.
AU - Kim, J.
N1 - Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.
PY - 1997/2/10
Y1 - 1997/2/10
N2 - 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 Q1 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.
AB - 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 Q1 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.
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U2 - 10.1017/s0022112096003965
DO - 10.1017/s0022112096003965
M3 - Article
AN - SCOPUS:0031080711
SN - 0022-1120
VL - 332
SP - 185
EP - 214
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -