Skip to main content
SpringerLink
Log in

Attributes of the large-scale coherent motions in a shear layer

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

PIV observations in a shear layer have been used to identify and characterize the discrete large-scale coherent motions (LSCMs) in the nominally self-preserving region: x/θo ≈ 450–610, of a shear layer. The LSCMs are given an objective definition wherein their centers are the (swirling flow pattern) nodes of the velocity-vector field as seen by an observer in the Galilean reference frame translating at an appropriately defined reference velocity. The statistical attributes of size, lateral location, and separation between these coherent motions (that exist in a single image) as well as their characteristic vorticity magnitude 〈ωmax〉 are reported.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Notes

  1. One can imagine a collapsed sphere as a deflated balloon. The associated vector field that is imprinted on the deflated balloon surface must be the same on the two flattened sides; hence, the vector field must be tangent at the perimeter except for the portion of the perimeter at which a hole is present. The balloon’s stem demonstrates the presence of a hole. An important constraint on the topological definition of a hole is that the components of the vector field that exist at and that are normal to the opening are uniformly directed onto or away from the subject sphere.

  2. Stokes theorem: \( \oint_{\text{c}} {\vec{V} \cdot d\vec{S}} = \iint_{A} {(\nabla \times \vec{V}) \cdot \hat{n}dA} \).

  3. The term transverse is used to indicate the “z” direction for the x-streamwise, y-spanwise coordinate system associated with the x–y plane PIV images.

  4. θ(x m) = 20 mm at the mid-point of the observational domain.

Abbreviations

C′:

Circulation contour limits (see Fig. 11)

L:

Data domain length (x d − x u) (see Fig. 16)

N:

Topologically defined node (see Fig. 9a)

N′:

Topologically defined half-node

S:

Topologically defined saddle (see Fig. 9a)

S′:

Topologically defined half-saddle (see Fig. 9b)

\( \bar{u}(x,y) \) :

Average velocity at location (x, y) (see Fig. 5)

\( \tilde{u}(x,y) \) :

RMS velocity at location (x, y) (see Fig. 5)

U o :

Free stream streamwise velocity (see Fig. 5)

U c :

Convection velocity (see Eq. 4)

V e :

Entrainment flow velocity

x:

Streamwise (downstream) flow direction (see Fig. 2)

y:

Spanwise direction (see Fig. 2)

z:

Out-of-plane direction

δ:

Edge length of PIV data domain (see Fig. 11)

δ(x):

Displacement thickness

δy c :

Distance from y c to the 0.5 Isotach at x = x c (see Figs. 11 and 6)

\( \mathcal{L} \) :

Circulation contour (square) side length (see Fig. 11)

\( \mathcal{L}^{*} \) :

Circulation side length where the data domain edge is reached

θ(x):

Momentum thickness (see Eq. 1a)

θ0 :

Momentum Thickness at the separation lip (backstep)

\( \Upgamma (\mathcal{L}) \) :

Circulation contour value for a surface (square) of side length \( (\mathcal{L}) \) (see Eq. 9)

〈ω〉:

Spatially averaged z–component vorticity magnitude (see Eq. 10)

χsurface :

Topologically defined surface characteristic number (see Eqs. 3a, 3b)

0.13:

Isotach 13 (see Fig. 6)

1.0:

Isotach 100 (see Fig. 6)

c:

Circulation contour center location (see Fig. 11)

d:

Downstream (x-direction) data domain boundary (see Sect. 5.3)

m:

Mid-location (x-direction) of the data domain (see Sect. 5.3)

max:

Associated with the maximum value of 〈ω〉; see Sect. 5.3

min:

2δ × 2δ area “patches” of 3 × 3 discrete velocity field vectors (see Sect. 5.5)

o:

Free stream regions

u:

Upstream (x-direction) data domain boundary (see Sect. 5.3)

References

  • Abrahamson S, Lonnes S (1995) Uncertainty in calculating vorticity from 2D velocity-fields using circulation and least-squares approaches. Exp Fluids 20(1):1–20

    Article  Google Scholar 

  • Adrian RJ, Christensen KT, Liu Z-C (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29:275–290

    Article  Google Scholar 

  • Bade KM (2007) Characterization of a shear layer through particle image velocimetry. MS Thesis, Michigan State University, Michigan

  • Barnard PS (2008) Grid-free simulation of the spatially growing turbulent mixing layer. AIAA J 46(7):1725–1737

    Article  Google Scholar 

  • Brown GL, Roshko A (1974) On density effects and large structure in turbulent mixing layers. J Fluid Mech 64:775–816

    Article  Google Scholar 

  • Cantwell BJ (1981) Organized motion in turbulent flow. Ann Rev Fluid Mech 13:457–515

    Article  Google Scholar 

  • Carlier J, Stanislas M (2005) Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J Fluid Mech 535:143–188

    Article  MATH  MathSciNet  Google Scholar 

  • Chakraborty P, Balachandar S (2006) Comment on ‘Axial stretching and vortex definition’ [Phys Fluids 17, 038108(2005]. Phys Fluids 18: 029101

    Google Scholar 

  • Chakraborty P, Balachandar S, Adrian RJ (2005) On the relationships between local vortex identification schemes. J Fluid Mech 535:189–214

    Article  MATH  MathSciNet  Google Scholar 

  • Champagne FH, Pao YH, Wygnanski IJ (1976) On the two-dimensional mixing region. J Fluid Mech 74:209–250

    Article  Google Scholar 

  • Cucitore R, Quadrio M, Baron A (1999) On the effectiveness and limitations of local criteria for the identification of a vortex. Eur J Mech B/Fluids 18:261–292

    Google Scholar 

  • Depardon S, Lasserre JJ, Brizzi LE, Borée J (2006) Instantaneous skin-friction pattern analysis using automated critical point detection on near-wall PIV data. Meas Sci Tech 17(7):1659–1669

    Article  Google Scholar 

  • Dimotakis PE (2005) Turbulent mixing. Ann Rev Fluid Mech 37:329–356

    Article  MathSciNet  Google Scholar 

  • Dimotakis P, Brown G (1976) The mixing layer at high Reynolds number: large-structure dynamics and entrainment. J Fluid Mech 78:535–560

    Article  Google Scholar 

  • Dimotakis PE, Debussy FD, Koochesfahani MM (1981) Particle streak velocity field measurements in a two-dimensional mixing layer. Phys Fluids 24(6):995–999

    Article  Google Scholar 

  • Druault P, Delville J, Bonnet J-P (2005) Experimental 3D analysis of the large scale behaviour of a plane turbulent mixing layer. Flow Turbulence Comb 74(2):207–233

    Article  Google Scholar 

  • Foss JF (2004) Surface selections and topological constraint evaluations for flow field analyses. Exp Fluids (Springer) 37:883–898. (Identified as F1 in text for brevity)

    Google Scholar 

  • Foss JF (2007) Topological considerations in fluid mechanics measurements. In: Tropea C, Yarin A, Foss J (eds), Springer handbook of experimental fluid mechanics. Chap 13, Springer, Berlin

  • Foss JF, Bohl DG, Kleis SJ (1995) Activity intermittency in a two-stream shear layer. In: Tenth symposium on turbulent shear flows. Pennsylvania State Univ., Pennsylvania

  • Gao Q, Ortiz-Duenas C, Longmire EK (2007) Circulation signature of vortical structures in turbulent boundary layers. In: 16th Australian Fluid Mechanics Conf

  • Haw RC, Foss JK, Foss JF (1989) Vorticity based intermittency measurements in a single stream shear layer. In: Fernholz H-H, Fiedler HE (eds) Advances in turbulence 2. Springer, Berlin

    Google Scholar 

  • Hellum AM, Foss JF (2007) Effects of flow scale on the intermittent properties of a single stream shear layer. In: 5th Int. Symposium on Turbulence and Shear Flow Phenomena, TU Munchen, Garching, Germany, 27–29 Aug, pp 1181–1186

  • Holmes P, Lumley JL, Berkooz G (1992) Coherent structures, symmetry, dynamical systems and turbulence. Cambridge University Press, Cambridge

    Google Scholar 

  • Hussain AKMF, Zaman KMBQ (1985) An experimental study of organized motions in the turbulent plane mixing layer. J Fluid Mech 159:85–104

    Article  Google Scholar 

  • Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94

    Article  MATH  MathSciNet  Google Scholar 

  • Liepmann DH, Laufer J (1947) Investigations of free turbulent mixing. NACA Tech. Note, 1257

  • Loth E (2008) Private communication: the vector field of Fig. 9

  • Morris SC (2002) The velocity and vorticity fields of a single stream shear layer. PhD Thesis, Michigan State University, Michigan

  • Morris SC, Foss JF (2003) Turbulent boundary layer to single-stream shear layer: the transition region. J Fluid Mech 494:187–221

    Article  MATH  Google Scholar 

  • Niccolls WO, Rockwell D (1972) Natural breakdown of planar jets. J Basic Eng 93(4):720–730

    Google Scholar 

  • Oakley TR, Loth E, Adrian RJ (1996) Cinematic particle image velocimetry of high-reynolds-number turbulent free shear layer. AIAA J 34(2):299–308

    Article  Google Scholar 

  • Rogers MM, Moser RD (1994) Direct simulation of a self-similar turbulent mixing layer. Phys Fluids 6(2):903–923

    Article  MATH  Google Scholar 

  • Roshko A (1976) Structure of turbulent shear flows: a new look. Dryden research lecture. AIAA J 14:1349–1357

    Article  Google Scholar 

  • Schmitt TP, Ali SK, Foss JF (1986) Relative efficiencies of parallel and perpendicular entrainment flow paths. AIAA J 24:1443–1444

    Article  Google Scholar 

  • Schneider K, Farge M, Pellegrino G, Rogers M (2005) Coherent vortex simulation of three-dimensional turbulent mixing layers using orthogonal wavelets. J Fluid Mech 534:39–66

    Article  MATH  MathSciNet  Google Scholar 

  • Wygnanski I, Fiedler HE (1970) The two-dimensional mixing region. J Fluid Mech 41(2):327–361

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA

    K. M. Bade & J. F. Foss

Authors
  1. K. M. Bade
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. F. Foss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. F. Foss.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bade, K.M., Foss, J.F. Attributes of the large-scale coherent motions in a shear layer. Exp Fluids 49, 225–239 (2010). https://doi.org/10.1007/s00348-010-0842-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-010-0842-z

Keywords

Search

Navigation