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REVIEW ARTICLES

Coherent Structures of Turbulence: Methods of Eduction and Results

[+] Author and Article Information
Giancarlo Alfonsi

Dipartimento di Difesa del Suolo,  Università della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italyalfonsi@dds.uncial.it

Appl. Mech. Rev 59(6), 307-323 (Nov 01, 2006) (17 pages) doi:10.1115/1.2345370 History:

In this paper the issue of the coherent structures of turbulence developing in wall-bounded flows is addressed. After a short historical synthesis, some basic concepts are reviewed and the idea of coherent structure is introduced. The phenomena occurring in the inner and outer regions of the turbulent boundary layer in conjunction with the most widely used event-detection techniques are considered, with reference to the large amount of mainly experimental results existing on the subject. The flow phenomena are described in terms of events occurring in the inner region, large-scale motions developing in the outer layer and dynamics of vortical structures. In the second part of the paper, methods for the eduction of the coherent structures of turbulence from the background flow and results obtained in the framework of each method are presented. The techniques involving the invariants of the velocity gradient tensor, the analysis of the Hessian of the pressure and the proper orthogonal decomposition are considered. Each procedure involves a particular definition of coherent structure that is supported by an appropriate mathematical framework and permits the analysis of a turbulent-flow database in terms of dynamics of coherent structures. This work may contribute to the dissemination of the most recent concepts and techniques now in use in turbulence research among fluid dynamicists.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Boundary-layer structure (adapted from Ref. 32). Symbols: bx,by, length scales of energetic near-wall eddies (see Ref. 43); Cb, celerity of energetic near-wall eddies (see Refs. 37,87,83,47,90); Cl, celerity of energetic outer-flow eddies (see Ref. 81); CL, celerity of the large-scale motions in the outer flow (see Refs. 81,87,92,83,47); lx,ly, length scales of energetic outer-flow eddies (see Refs. 88,92); Lx,Ly, length scales of the large-scale motions in the outer flow (see Refs. 42,87-88,92,89,57,47); Xb, persistence distance of energetic near-wall eddies (see Ref. 57); Xl, persistence distance of energetic outer-flow eddies; XL, persistence distance of large-scale motions in the outer flow (see Ref. 81); and λy, vertical half-scale of sublayer structure (see Refs. 37,81,64).

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Figure 2

Idealized scheme of the distribution of vortical structures in the different regions of a turbulent boundary layer (adapted from Ref. 31)

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Figure 11

Idealized scheme of nested packets of hairpin vortices growing up from the wall (adapted from Ref. 136). The packets align in the streamwise direction and large-scale motions in the wake region limit their growth. Symbols: Uci, convection velocities in the streamwise direction.

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Figure 12

Conceptual model of an array of coherent structures in the near-wall region of a turbulent channel flow, detected using the criterion of the analysis of the Hessian of the pressure (adapted from Ref. 137): (a) top view; (b) side view. Symbols: SP, quasi-streamwise structures with positive vorticity in the streamwise direction; SN, quasi-streamwise structures with negative vorticity in the streamwise direction; Q2, second-quadrant event (ejection); and Q4, fourth-quadrant event (sweep).

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Figure 13

Surfaces of constant streamwise velocity of POD-generated “propagating modes” in minimal channel flow (adapted from Ref. 114). The light surfaces represent positive streamwise velocity and the dark surfaces represent negative streamwise velocity.

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Figure 10

Vortical structures detected from turbulent-channel-flow data using the criterion of the “imaginary part of the complex eigenvalue pair of the velocity gradient tensor” (adapted from Ref. 19). Symbols: PHV, primary hairpin vortex; SHV, secondary hairpin vortex; THV, tertiary hairpin vortex; DHV, downstream hairpin vortex; QSV, quasi-streamwise vortex; and Ci, cross sections.

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Figure 9

Vortical structures detected from turbulent-channel-flow data using the criterion of the “positive values of the second invariant of the velocity gradient tensor” (adapted from Ref. 135)

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Figure 8

Vortical structures detected from data for zero-pressure-gradient flow using the criterion of the “complex eigenvalues of the velocity gradient tensor” (adapted from Ref. 131)

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Figure 7

Vortical structures in the boundary layer (adapted from Ref. 31). Symbols: u′ν′2, second-quadrant event (ejection); u′ν′4, fourth-quadrant event (sweep).

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Figure 6

Evolution of hairpin vortices in the boundary layer (adapted from Ref. 100)

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Figure 5

Hairpin vortex model after Theodorsen (see Ref. 97) (adapted from Ref. 36)

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Figure 4

Generation of secondary hairpins from primary symmetric hairpin vortices (adapted from Ref. 101)

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Figure 3

Generation of low-speed streaks caused by hairpin vortices (adapted from Ref. 101)

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