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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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References

Antonia, R. A. & Bisset, D. K. 1990 Spanwise structure in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 210, 437.CrossRefGoogle Scholar
Batchelor, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bernard, P. S., Thomas, J. M. & Handler, R. A. 1993 Vortex dynamics and the production of Reynolds stress. J. Fluid Mech. 253, 385.CrossRefGoogle Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269.CrossRefGoogle Scholar
Blackwelder, R. F. & Eckelman, H. 1979 Streamwise vortices associated with the bursting phenomenon. Part 3. J. Fluid Mech. 94, 577.CrossRefGoogle Scholar
Blackwelder, R. F. & Kaplan, R. E. 1976 On the wall structure of the turbulent boundary layer J. Fluid Mech. 76, 89.CrossRefGoogle Scholar
Bogard, D. G. & Tiederman, W. G. 1986 Burst detection with single-point velocity measurement. J. Fluid Mech. 162, 389.CrossRefGoogle Scholar
Brooke, J. W. & Hanratty, T. J. 1993 Origin of turbulence-producing eddies in a channel flow. Phys. Fluids A 5, 1011.CrossRefGoogle Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow field. Phys. Fluids A 2, 765.CrossRefGoogle Scholar
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1.CrossRefGoogle Scholar
Fiedler, H. E. 1988 Coherent structures in turbulent flows. Prog. Aero. Sci. 25, 231.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317.CrossRefGoogle Scholar
Hayakawa, M. 1992 Vorticity-based conditional sampling for identification of large-scale vortical structures in turbulent shear flows. In Eddy Structure Identification in Free Turbulent Shear Flows (ed. Bonnet, J. P. & Glauser, M. N.), p. 45. Kluwer.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-SSS, p. 193.Google Scholar
Husain, H. & Hussain, F. 1993 Elliptic jets. Part 3. Dynamics of preferred mode coherent structure. J. Fluid Mech. 248, 315.CrossRefGoogle Scholar
Hussain, A. K. M. F. 1980 Coherent structure and studies of perturbed and unperturbed jets. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. Jimenez, J.), p. 136. Springer.Google Scholar
Hussain, A. K. M. F. 1983a Coherent structures — reality and myth. Phys. Fluids 26, 2816.Google Scholar
Hussain, A. K. M. F. 1983b Coherent structures and incoherent turbulence. In Turbulence and Chaotic Phenomena in Fluids, (ed. Tatsumi, T.), p. 453. North-Holland.Google Scholar
Hussain, A. K. M. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303.CrossRefGoogle Scholar
Hussain, A. K. M. F. & Hayakawa, M. 1987 Eduction of large-scale organized structures in a turbulent plane wake. J. Fluid Mech. 180, 193.CrossRefGoogle Scholar
Hussain, F., Jeong, J. & Kim, J. 1987 Structure of turbulent shear flows. Center for Turbulence Research Report CTR-SS1, p. 273.Google Scholar
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1980 Vortex pairing in a circular jet under controlled excitation, Part 2. Coherent structure dynamics. J. Fluid Mech. 101, 493.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1992 Coherent structure near the wall in a turbulent channel flow. Proc. of Fifth Asian Congress of Fluid Mech., Taejon, Korea (ed. Chang, K. S. & Choi, H.), p. 1262.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69.CrossRefGoogle Scholar
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213.CrossRefGoogle Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579.CrossRefGoogle Scholar
Kida, S. & Tanaka, M. 1994 Dynamics of vortical structures in a homogeneous shear flow, J. Fluid Mech. 274, 43.CrossRefGoogle Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421.CrossRefGoogle Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids A 5, 695.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133.CrossRefGoogle Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA 731–78.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Rundstadler, P. W. 1967 The structure of turbulent boundary layer. J. Fluid Mech. 30, 741.CrossRefGoogle Scholar
Kline, S. J. & Robinson, S. K. 1989 Turbulent boundary layer structure: progress, status and challenges. Proc. IUTAM Symp. Struct, of Turbulence and Drag Reduction, Zurich. Google Scholar
Melander, M. V. & Hussain, F. 1994 Core dynamics on a vortex column. Fluid Dyn. Res. 13, 1.CrossRefGoogle Scholar
Mumford, J. C. 1982 The structure of large eddies in fully developed turbulent shear flows. Part 2. The plane wake. J. Fluid Mech. 137, 447.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 23, 601.CrossRefGoogle Scholar
Schoppa, W. 1997 PhD dissertation, University of Houston (in preparation).Google Scholar
Schoppa, W., Hussain, F. & Metcalfe, R. W. 1995 A new mechanism of small-scale transition in a plane mixing layer: core dynamics of spanwise vortices. J. Fluid Mech. 298, 23.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re = 1410. J. Fluid Mech. 187, 61.CrossRefGoogle Scholar
Stretch, D. 1989 Patterns in simulated turbulent channel flow. Center for Turbulence Research Report CTR-SS9, p. 261.Google Scholar
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 225.CrossRefGoogle Scholar
Tennekes, T. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Townsend, A. A. 1979 Flow patterns of large eddies in a wake and in a boundary layers. J. Fluid Mech. 95, 515.CrossRefGoogle Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65.CrossRefGoogle Scholar