Turbulent Shear Flows 5 pp 110-123 | Cite as

# Coherent Structures in a Turbulent Mixing Layer: A Comparison Between Direct Numerical Simulations and Experiments

## Abstract

An eduction scheme has been developed in an attempt to determine the characteristics of large-scale vortical structures in a turbulent mixing layer. This analysis scheme has been applied to a set of experimental data taken in a new, large mixing layer facility designed to minimize boundary and resonance effects. The scheme is based on detection of large-scale vorticity concentrations from smoothed vorticity maps, accepting structures of certain size and strength and aligning the realizations through correlation of vorticity. A similar scheme has been developed to apply to the results of a direct numerical simulation of a temporally growing mixing layer. A comparison of the two approaches shows important similarities in details of the coherent structures educed both ways. The numerical simulations indicate that low levels of coherent forcing can dramatically change the evolution of the mixing layer. In the absence of such forcing, the numerical simulations and experiments show a lack of regularity in the transverse position, spacing, amplitude, shape and spanwise coherence of the large-scale vortical structures.

## Keywords

Direct Numerical Simulation Turbulent Boundary Layer Coherent Structure Vortex Pairing Streamwise Vortex## Nomenclature

- Re
_{λ}) Reynolds number based on Taylor microscale

- RE
_{x}) Reynolds number =

*xU*_{ e }/*v*- S̄
_{M}) Peak mean shear rate =\({\left. {\frac{{\partial U}} {{\partial y}}} \right|_{\max }}\)

- T̄)
=

*t U*_{ c }/*θ*- T̄)
=

*t S̄*_{ Mo }- U)
Mean velocity difference (simulations)

- U
_{c}) Streamwise advection velocity of coherent structures (experiments) = 0.5

*U*_{ e }- U
_{e}) Mean exit velocity (experiment)

- Ū(y))
Mean velocity

- u′ v′ w′)
rms perturbation velocities

- u
_{c}, v_{c}) Coherent velocity fields

- u
_{r}, v_{r}) Incoherent velocity fields

- x, y, z)
Streamwise, transverse and spanwise coordinates

- Y)
= y/θ

- δ
_{ω}) Mean vorticity thickness =

*U*_{ e }/*S*_{ M }- θ)
Local momentum thickness

- θ
_{e}) Exit boundary layer momentum thickness (experiment)

- λ)
Wavelength of fundamental (most unstable) mode

- ω)
Vorticity

## Preview

Unable to display preview. Download preview PDF.

## References

- Bernal, L. P. (1981): “The Coherent Structure of Turbulent Mixing Layers. I. Similarity of the Primary Vortex Structure. II. Secondary Streamwise Vortex Structure;” Ph. D. Thesis, California Institute of TechnologyGoogle Scholar
- Breidenthal, R. (1981): Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech.
**109**, 1–24ADSCrossRefGoogle Scholar - Brown, G. L., Roshko, A. (1974): On density effects and large structure in turbulent mixing layers. J. Fluid Mech.
**64**, 775–816ADSCrossRefGoogle Scholar - Gottlieb, D., Orszag, S. (1977): Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied MathematicsMATHCrossRefGoogle Scholar
- Ho, C. M., Huerre, P. (1984): Perturbed free shear layers. Ann. Rev. Fluid Mech.
**16**, 365–424ADSCrossRefGoogle Scholar - Hussain, A. K. M. F. (1983): “Coherent Structures and Incoherent Turbulence,” in
*Turbulence and Chaotic Phenomena in Fluids*, ed. by T. Tatsumi (North Holland, Amsterdam) pp. 245–249Google Scholar - Hussain, A. K. M. F. (1985): “Measurements of Large Scale Organized Motions in Turbulent Flows,” in
*Forum on Unsteady Flows in Biological Systems*, ed. by M. H. Friedman, D. C. Wiggert, ASME, 8–12Google Scholar - Hussain, A. K. M. F., Zaman, K. B. M. Q. (1981 a): The ‘Preferred Mode’ of the axisymmetric jet. J. Fluid Mech.
**110**, 39–71ADSCrossRefGoogle Scholar - Hussain, A. K. M. F., Zaman, K. B. M. Q. (1981 b): The natural large-scale coherent structure in an initially turbulent mixing layer. Bull. Am. Phys. Soc.
**26**, 1273Google Scholar - Hussain, A. K. M. F., Zaman, K. B. M. Q. (1985): An experimental study of organized motions in the turbulent plane mixing layer. J. Fluid Mech.
**159**, 85–104ADSCrossRefGoogle Scholar - Kleis, S., Hussain, A. K. M. F. (1979): The asymptotic state of the plane mixing layer. Bull. Am. Phys. Soc.
**24**, 1132Google Scholar - Lin, S. J., Corcos, G. M. (1984): The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech.
**141**, 139–178ADSMATHCrossRefGoogle Scholar - Michalke, A. (1964): On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech.
**19**, 543–556MathSciNetADSMATHCrossRefGoogle Scholar - Pierrehumbert, R. T., Widnall, S. E. (1982): The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech.
**114**, 59–82ADSMATHCrossRefGoogle Scholar - Riley, J. J., Metcalfe, R. W. (1979): “Direct Numerical Simulations of the Turbulent Wake of an Axisymmetric Body,” in
*Turbulent Shear Flows 2*, ed. by L. J. S. Bradbury et al. (Springer, Berlin, Heidelberg) pp. 78–93Google Scholar - Riley, J. J., Metcalfe, R. W. (1980): Direct numerical simulation of a perturbed turbulent mixing layer. AIAA Paper 80–0274Google Scholar
- Wygnanski, I., Fiedler, H. E. (1970): The two-dimensional mixing region. J. Fluid Mech.
**41**, 327–361ADSCrossRefGoogle Scholar - Wygnanski, I., Oster, D., Fiedler, H. (1979): “A Forced, Plane, Turbulent Mixing-Layer; A Challenge for the Predictor,” in
*Turbulent Shear Flows 2*, ed. by L. J. S. Bradbury et al. (Springer, Berlin, Heidelberg) pp. 314–326Google Scholar - Zaman, K. B. M. Q., Hussain, A. K. M. F. (1977): “Vortex Pairing and Organized Structures in Circular Jets Under Controlled Excitation,”
*Turbulent Shear Flows I*, Penn. State Univ., pp. 11.23–11.31Google Scholar - Zaman, K. B. M. Q., Hussain, A. K. M. F. (1980): Vortex pairing and organized structures in circular jets under controlled excitation. J. Fluid Mech.
**101**, 449–492ADSCrossRefGoogle Scholar - Zaman, K. B. M. Q., Hussain, A. K. M. F. (1984): “Natural large-scale structures in the axisymmetric mixing layer. J. Fluid Mech.
**138**, 325–351ADSCrossRefGoogle Scholar