Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-01T11:34:44.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Reynolds stress and the physics of turbulent momentum transport

Published online by Cambridge University Press:  26 April 2006

Peter S. Bernard  and
Robert A. Handler
Peter S. Bernard
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
Robert A. Handler
Affiliation:
Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Washington, DC 20375, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The nature of the momentum transport processes responsible for the Reynolds shear stress is investigated using several ensembles of fluid particle paths obtained from a direct numerical simulation of turbulent channel flow. It is found that the Reynolds stress can be viewed as arising from two fundamentally different mechanisms. The more significant entails transport in the manner described by Prandtl in which momentum is carried unchanged from one point to another by the random displacement of fluid particles. One-point models, such as the gradient law are found to be inherently unsuitable for representing this process. However, a potentially useful non-local approximation to displacement transport, depending on the global distribution of the mean velocity gradient, may be developed as a natural consequence of its definition. A second important transport mechanism involves fluid particles experiencing systematic accelerations and decelerations. Close to the wall this results in a reduction in Reynolds stress due to the slowing of sweep-type motions. Further away Reynolds stress is produced in spiralling motions, where particles accelerate or decelerate while changing direction. Both transport mechanisms appear to be closely associated with the dynamics of vortical structures in the wall region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 99 - 124
Copyright
© 1990 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

Azab, K. A. & Mclaughlin, J. B., 1987 Modeling the viscous wall region. Phys. Fluids 30, 2362–2373.Google Scholar
Bernard, P. S., Ashmawey, M. F. & Handler, R. A., 1989a Evaluation of the gradient model of turbulent transport through direct Lagrangian simulation. AIAA J. 27, 1290–1292.Google Scholar
Bernard, P. S., Ashmawey, M. F. & Handler, R. A., 1989b An analysis of particle trajectories in computer simulated turbulent channel flow. Phys. Fluids A 1, 1532–1540.Google Scholar
Brodkey, R. S., Wallace, J. M. & Eckelmann, H., 1974 Some properties of truncated turbulence signals in bounded shear flows. J. Fluid Mech. 63, 209–224.Google Scholar
Corrsin, S.: 1974 Limitations of gradient transport models in random walks and turbulence. Adv. Geophys. 18A, 25–60.Google Scholar
Deardorff, J. W. & Peskin, R. L., 1970 Lagrangian statistics from numerically integrated turbulent shear flow. Phys. Fluids 13, 584–595.Google Scholar
Handler, R. A., Hendricks, E. W. & Leighton, R. I., 1989 Low Reynolds number calculation of turbulent channel flow: a general discussion. Naval Research Laboratory Mem. Rep. 6410.Google Scholar
Hinze, J. O.: 1975 Turbulence, 2nd edn. McGraw-Hill.
Kim, J., Moin, P. & Moser, R., 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Lakshminarayana, B.: 1986 Turbulence modeling for complex shear flows. AIAA J. 24, 1900–1917.Google Scholar
Lumley, J.: 1983 Turbulence modeling. J. Appl. Mech. 50, 1097–1103.Google Scholar
Marcus, P. S.: 1984 Simulation of Taylor–Couette flow. Part 1. Numerical methods and comparison with experiment. J. Fluid Mech. 146, 45–64.Google Scholar
Orszag, S. A. & Kells, L. C., 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Peskin, R. L.: 1974 Numerical simulation of Lagrangian turbulent quantities in two and three dimensions. Adv. Geophys. 18A, 141–163.Google Scholar
Piomelli, U., Moin, P. & Ferziger, J., 1989 Large eddy simulation of the flow in a transpired channel. AIAA paper 89–0375.Google Scholar
Prandtl, L.: 1925 Über die ausgebildete Turbulenz. Z. Angew. Math. Mech. 5, 136–138.Google Scholar
Robinson, S., Kline, S. J. & Spalart, P. R., 1988 Quasi-coherent structures in the turbulent boundary layer. Proc. Zaric Memorial Intl Sem. on Near-Wall Turbulence, Dubrovnik, Yugoslavia. Hemisphere.Google Scholar
Speziale, C. G.: 1987 On nonlinear K–l and K–ε models of turbulence. J. Fluid Mech. 178, 459–475.Google Scholar
Taylor, G. I.: 1915 Eddy motion in the atmosphere. Phil. Trans. R. Soc. Lond. 215, 1–26.Google Scholar
Taylor, G. I.: 1932 The transport of vorticity and heat through fluids in turbulent motion. Proc. R. Soc. Lond. A 135, 685–705.Google Scholar
Tennekes, H. & Lumley, J. L., 1972 A First Course in Turbulence. MIT Press.
Wallace, J. M.: 1985 The vortical structure of bounded turbulent shear flow. In Flow of Real Fluids. Lecture Notes in Physics, vol. 235, pp. 253–268. Springer.
Yeung, P. K. & Pope, S. B., 1988 An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79, 373–416.Google Scholar