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

Vortex Coherence Vorticity Advection### 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

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