Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-29T22:26:06.906Z Has data issue: false hasContentIssue false
  • English
  • Français

The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties

Published online by Cambridge University Press:  26 April 2006

Jean-Louis Balint ,
James M. Wallace  and
Petar Vukoslavčević
Jean-Louis Balint
Affiliation:
Department of Mechanical Engineering, The University of Maryland, College Park, MD 20742, USA
James M. Wallace
Affiliation:
Department of Mechanical Engineering, The University of Maryland, College Park, MD 20742, USA
Petar Vukoslavčević
Affiliation:
Department of Mechanical Engineering, The University of Maryland, College Park, MD 20742, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Many of the statistical properties of both the velocity and the vorticity fields of a nominally zero-pressure-gradient turbulent boundary layer at Rδ = 27650 (Rθ = 2685) have been simultaneously measured. The measurements were made with a small nine-sensor hot-wire probe which can resolve the turbulence to within about six Kolmogorov microscales just above the sublayer. The statistical properties of the velocity vector field compare very well with other laboratory measurements and with direct numerical simulations when Reynolds-number dependence is taken into account. The statistical properties of the vorticity field are also in generally good agreement with the few other measurements and with the direct numerical simulations available for comparison. Near the wall, r.m.s. measurements show that the fluctuating spanwise vorticity is the dominant component, but in the outer part of the boundary layer all the component r.m.s. values are nearly equal. R.m.s. measurements of the nine individual velocity gradients show that the gradients normal to the wall of all three velocity components are the largest, with peaks occurring near the wall as expected. Gradients in the streamwise direction are everywhere small. One-dimensional spectra of the vorticity components show the expected shift of the maximum energy to higher wavenumbers compared to spectra of the velocity components at the same location in the flow. The budget of the transport equation for total enstrophy indicates that the viscous dissipation rate is primarily balanced by the viscous diffusion rate in the buffer layer and by the rotation and stretching rate in the logarithmic layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 228 , July 1991 , pp. 53 - 86
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balint, J.-L., Vukoslavčević, P. & Wallace, J. M. 1987 A study of the vortical structure of the turbulent boundary layer. In Advances in Turbulence (ed. G. Comte-Bellot & J. Mathieu), pp. 456–464. Springer.
Balint, J.-L., Vukoslavčević, P. & Wallace, J. M. 1990 The transport of enstrophy in a turbulent bounary layer. In Near Wall Turbulence (ed. S. J. Kline & N. Afgan), pp. 932–950. Hemisphere.
Coles, D. E. 1962 The turbulent boundary layer in compressible fluid. Appendix A: A manual of experimental practice for low speed flow. Rand Rep. R403R-PR, ARC24473.Google Scholar
Corrsin, S. 1953 Interpretation of viscous terms in the turbulent energy equation. J. Aeronaut. Sci. 12, 853–854.Google Scholar
Foss, J. F. 1981 Advanced techniques for transverse vorticity measurements In Proc. 7th Biennial Symp. on Turbulence, University of Missouri-Rolla, pp. 208–218.
Gresko, L. S. 1988 Characteristics of wall pressure and near-wall velocity in a flat plate turbulent boundary layer. S.M. Thesis, MIT.
Karlsson, R. I. & Johansson, T. G. 1988 LDV measurements of higher order moments of velocity fluctuation in a turbulent boundary layer In Laser Anemometry in Fluid Mechanics. Ladoan-Instituto Superior Technico, Lisbon, Portugal.
Kastrinakis, E. G. & Eckelmann, H. 1983 Measurement of streamwise vorticity fluctuations in a turbulent channel flow. J. Fluid Mech. 137, 165–186.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds numbers. J. Fluid Mech. 177, 133–166.Google Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN3178.Google Scholar
Klewicki, J. C. 1989 On the interactions between the inner and outer region motions in turbulent boundary layers. Ph.D. Dissertation, Michigan State University.
Mansour, N. N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.Google Scholar
Piomelli, U., Balint, J.-L. & Wallace J, M. 1989 On the validity of Taylor's hypothesis for wall-bounded turbulent flows.. Phys. Fluids A 1, 609–611.Google Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds numbers. Phys. Fluids 24, 802–811.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalding, D. B. 1961 A single formula for the law of the wall. Trans. ASME C: J. Appl. Mech. 28, 455–458.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Vukoslavčević, P. & Wallace, J. M. 1981 Influence of velocity gradients on measurements of velocity and streamwise vorticity with hot-wire X-array probes. Rev. Sci. Instrum. 52, 869–879.Google Scholar
Vukoslavčević, P., Wallace, J. M. & Balint, J.-L. 1991 The velocity and vorticity vector fields of a turbulent boundary layer. Part 1. Simultaneous measurement by hot-wire anemometry. J. Fluid Mech. 228, 25–51.Google Scholar
Wei, T. 1987 Reynolds number effects on the small scale structure of a turbulent channel flow. Ph.D. Dissertation, The University of Michigan.
Wei, T. & Willmarth, W. W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.Google Scholar