Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers

A similarity relationship is proposed to describe the streamwise broadband-turbulence intensity in a zero-pressure-gradient boundary layer. The formulation is applicable to the entire region of the flow beyond the viscous buffer zone and is based on the attached eddy hypothesis, the Reynolds-number-similarity hypothesis and the assumed existence of Kolmogorov eddies with a universal inertial subrange. Experimental data of the authors and those from various published works covering a large Reynolds number range are investigated in light of this formulation.

[1]  S. J. Kline,et al.  Near-Wall Turbulence: 1988 Zoran Zaric Memorial Conference , 1989 .

[2]  Peter N. Joubert,et al.  Low-Reynolds-number turbulent boundary layers , 1991, Journal of Fluid Mechanics.

[3]  A. Perry,et al.  A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support , 1995, Journal of Fluid Mechanics.

[4]  Effect of Reynolds Number on the Structure of Turbulent Boundary Layers , 1994 .

[5]  George P. Huang,et al.  The law of the wall in turbulent flow , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[6]  M. S. Chong,et al.  On the mechanism of wall turbulence , 1982, Journal of Fluid Mechanics.

[7]  A. Perry,et al.  Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes , 1977, Journal of Fluid Mechanics.

[8]  D. Coles.  The law of the wake in the turbulent boundary layer , 1956, Journal of Fluid Mechanics.

[9]  Mohamed Gad-el-Hak,et al.  Reynolds Number Effects in Wall-Bounded Turbulent Flows , 1994 .

[10]  Ivan Marusic,et al.  A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis , 1995, Journal of Fluid Mechanics.

[11]  J. D. Li,et al.  Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers , 1990, Journal of Fluid Mechanics.

[12]  F. Durst,et al.  LDA measurements in the near-wall region of a turbulent pipe flow , 1995, Journal of Fluid Mechanics.

[13]  P. Spalart.  Direct simulation of a turbulent boundary layer up to Rθ = 1410 , 1988, Journal of Fluid Mechanics.

[14]  Alexander J. Smits,et al.  Turbulent Shear Layers in Supersonic Flow , 1996 .

[15]  Peter Bradshaw,et al.  The turbulence structure of equilibrium boundary layers , 1967, Journal of Fluid Mechanics.

[16]  H. H. Fernholz,et al.  The incompressible zero-pressure-gradient turbulent boundary layer: An assessment of the data , 1996 .

[17]  A. Tsinober,et al.  Hot Wire Anemometry , 1995 .

[18]  A. Townsend,et al.  Equilibrium layers and wall turbulence , 1961, Journal of Fluid Mechanics.

[19]  A. Perry,et al.  An experimental study of the turbulence structure in smooth- and rough-wall boundary layers , 1987, Journal of Fluid Mechanics.

[20]  M. S. Chong,et al.  A theoretical and experimental study of wall turbulence , 1986, Journal of Fluid Mechanics.

[21]  Reynolds-number dependence of the structure of a turbulent boundary layer , 1982 .

[22]  The attached eddy hypothesis in wall turbulence , 1990 .

[23]  L. Kovasznay.  Spectrum of Locally Isotropic Turbulence , 1948 .

[24]  A. Townsend.  The Structure of Turbulent Shear Flow , 1975 .

[25]  M. S. Chong,et al.  Topology of flow patterns in vortex motions and turbulence , 1994 .

[26]  F. A. Schraub,et al.  The structure of turbulent boundary layers , 1967, Journal of Fluid Mechanics.

[27]  J. D. Li,et al.  Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis , 1994 .

[28]  E. Krause,et al.  Comparative measurements in the canonical boundary layer at Reδ2≤6×104 on the wall of the German–Dutch windtunnel , 1995 .

[29]  Philippe R. Spalart,et al.  Experimental and numerical study of a turbulent boundary layer with pressure gradients , 1993, Journal of Fluid Mechanics.

[30]  F. Nieuwstadt,et al.  Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence , 1996 .

[31]  W. Phillips.  The wall region of a turbulent boundary layer , 1987 .