Research Papers: Fundamental Issues and Canonical Flows

Self-Similarity Analysis of Turbulent Wake Flows

[+] Author and Article Information
Tie Wei

Department of Mechanical Engineering,
New Mexico Institute of Mining and Technology,
Socorro, NM 87801
e-mail: tie.wei@nmt.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 8, 2016; final manuscript received December 1, 2016; published online March 16, 2017. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 139(5), 051203 (Mar 16, 2017) (6 pages) Paper No: FE-16-1223; doi: 10.1115/1.4035633 History: Received April 08, 2016; Revised December 01, 2016

This paper investigates the self-similarity properties in the far downstream of high Reynolds number turbulent wake flows. The growth rate of the wake layer width, dδ/dx; the decaying rate of the maximum velocity defect, dUs/dx; and the scaling for the maximum mean transverse (across the stream) velocity, Vmax, are derived directly from the self-similarity of the continuity equation and the mean momentum equation. The analytical predictions are validated with the experimental data. Using an approximation function for the mean axial flow, the self-similarity analysis yields approximate solutions for the mean transverse velocity, V, and the Reynolds shear stress, T=uv. Close relations among the shapes of U, V, and T are revealed.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Townsend, A. A. , 1980, The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, UK.
Wygnanski, I. , Champagne, F. , and Marasli, B. , 1986, “ On the Large-Scale Structures in Two-Dimensional, Small-Deficit, Turbulent Wakes,” J. Fluid Mech., 168, pp. 31–71. [CrossRef]
Pope, S. B. , 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Wilcox, D. C. , 2006, Turbulence Modeling for CFD, 3rd ed., DCW Industries, La Canada, CA.
George, W. K. , 1989, “ The Self-Preservation of Turbulent Flows and Its Relation to Initial Conditions and Coherent Structures,” Adv. Turbul., pp. 39–73.
Antonia, R. , and Mi, J. , 1998, “ Approach Towards Self-Preservation of Turbulent Cylinder and Screen Wakes,” Exp. Therm. Fluid Sci., 17(4), pp. 277–284. [CrossRef]
George, W. K. , 2012, “ Asymptotic Effect of Initial and Upstream Conditions on Turbulence,” ASME J. Fluids Eng., 134(6), p. 061203. [CrossRef]
Schlichting, H. , and Gersten, K. , 2000, Boundary-Layer Theory, Springer-Verlag, Berlin.
Sreenivasan, K. , 1981, “ Approach to Self-Preservation in Plane Turbulent Wakes,” AIAA J., 19(10), pp. 1365–1367. [CrossRef]
Sreenivasan, K. R. , and Narasimha, R. , 1982, “ Equilibrium Parameters for Two-Dimensional Turbulent Wakes,” ASME J. Fluids Eng., 104(2), pp. 167–169. [CrossRef]
Ong, L. , and Wallace, J. , 1996, “ The Velocity Field of the Turbulent Very Near Wake of a Circular Cylinder,” Exp. Fluids, 20(6), pp. 441–453. [CrossRef]
Ma, X. , Karamanos, G.-S. , and Karniadakis, G. , 2000, “ Dynamics and Low-Dimensionality of a Turbulent Near Wake,” J. Fluid Mech., 410, pp. 29–65. [CrossRef]
Konstantinidis, E. , Balabani, S. , and Yianneskis, M. , 2005, “ Conditional Averaging of PIV Plane Wake Data Using a Cross-Correlation Approach,” Exp. Fluids, 39(1), pp. 38–47. [CrossRef]
Yang, J. , Liu, M. , Wu, G. , Zhong, W. , and Zhang, X. , 2014, “ Numerical Study on Coherent Structure Behind a Circular Disk,” J. Fluids Struct., 51, pp. 172–188. [CrossRef]
Gough, T. , and Hancock, P. , 1996, “ Low Reynolds Number Turbulent Near Wakes,” Advances in Turbulence VI, Springer, The Netherlands, pp. 445–448.
Hickey, J.-P. , 2012, “ Direct Simulation and Theoretical Study of Sub-and Supersonic Wakes,” Ph.D. thesis, Royal Military College of Canada, Ontario, Canada.
Liu, X. , 2001, “ A Study of Wake Development and Structure in Constant Pressure Gradients,” Ph.D. thesis, University of Notre Dame, Notre Dame, IN.


Grahic Jump Location
Fig. 2

Transverse distribution of the mean flow in the far-wake of turbulent wake flows. (a) The mean axial velocity defect profile, f≡(U∞−U)/Us. (b) Mean transverse velocity and Reynolds shear stress. Experimental data are from Ref. [2] (WCM), Ref. [16] (Hickey), Ref. [17] (Liu), Ref. [15] (GH at two downstream locations, x = 1 m and x = 0.58 m), and Ref. [11] (OW). Note that the Reynolds shear stress should be antisymmetric. GH (x = 0.58 m) data at positive y agree well with the two other data, but not in the negative y.

Grahic Jump Location
Fig. 1

Schematic of a statistically two-dimensional stationary wake flow (statistics do not vary in the third, z−, direction). Thedominant direction of mean flow is in the axial direction, x, and the cross-stream coordinate is y. Mean velocity along thecenterline is denoted as Uc, where the velocity defect is maximum, Us=U∞−Uc. Wake half-width, δ=y0.5, is defined as U(y0.5)=U∞−0.5Us.

Grahic Jump Location
Fig. 4

Experimental data of g/(ηf). The difference between the values at x=0.34 m, and the rest is attributed to the near-wake effect.

Grahic Jump Location
Fig. 3

The mean axial velocity defect, f, along with curves of Gaussian function e−aη2. Curves with three different constants a=0.6,0.7,0.8 are plotted. The curve with a = 0.7 seems to fit the data better.

Grahic Jump Location
Fig. 5

Scaling of the maximum mean transverse velocity, Vmax, in the far downstream of turbulent wake flow

Grahic Jump Location
Fig. 6

Approximation function for the mean transverse velocity, g=V/Vmax≈−2ηe−aη2

Grahic Jump Location
Fig. 7

Approximation function for the Reynolds shear stress, h=T/Us2≈0.092ηe−aη2

Grahic Jump Location
Fig. 8

(a) Relation between V and U. Solid symbols are data of V/Vmax, and open symbols are data of −2ηf. (b) Relation between T and U. Solid symbols are data of T/Us2, open symbols 0.092ηf. (c) Relation between T and V. Solid symbols are data of −T/Us2 and open symbols (V/Us)(U∞/Us).



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In