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Fluid particle dynamics and the non-local origin of the Reynolds shear stress

Published online by Cambridge University Press:  23 May 2018

Peter S. Bernard Open the ORCID record for Peter S. Bernard [Opens in a new window]  and
Martin A. Erinin
Peter S. Bernard*
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
Martin A. Erinin
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: [email protected]
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Abstract

The causative factors leading to the Reynolds shear stress distribution in turbulent channel flow are analysed via a backward particle path analysis. It is found that the classical displacement transport mechanism, by which changes in the mean velocity field over a mixing time correlate with the wall-normal velocity, is the dominant source of Reynolds shear stress. Approximately 20 % of channel flow at any given time contains fluid motions that contribute to displacement transport. Much rarer events provide a small but non-negligible contribution to the Reynolds shear stress due to fluid particle accelerations and long-lived correlations deriving from structural features of the near-wall flow. The Reynolds shear stress in channel flow is shown to be a non-local phenomenon that is not conducive to description via a local model and particularly one depending directly on the local mean velocity gradient.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 520 - 551
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Copyright
© 2018 Cambridge University Press 

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References

Araya, G. & Castillo, L. 2012 DNS of turbulent thermal boundary layers up to Re 𝜃 = 2300. Intl J. Heat Mass Transfer 55, 4003–4019.Google Scholar
Bernard, P. S. 2013 Vortex dynamics in transitional and turbulent boundary layers. AIAA J. 51, 1828–1842.CrossRefGoogle Scholar
Bernard, P. S. & Handler, R. A. 1990 Reynolds stress and the physics of turbulent momentum transport. J. Fluid Mech. 220, 99–124.Google Scholar
Bernard, P. S., Thomas, J. M. & Handler, R. A. 1993 Vortex dynamics and the production of Reynolds stress. J. Fluid Mech. 253, 385–419.Google Scholar
Bernard, P. S. & Wallace, J. M. 2002 Turbulent Flow: Analysis, Measurement and Prediction. Wiley.Google Scholar
Boudjemadi, R., Maupu, V., Laurence, D. & Qur, P. L. 1997 Budgets of turbulent stresses and fluxes in a vertical slot natural convection flow at Rayleigh Ra = 105 and 5. 4 105 . Intl J. Heat Fluid Flow 18, 70–79.Google Scholar
Corrsin, S. 1974 Limitations of gradient transport models in random walks and turbulence. Adv. Geophys. 18A, 25–60.Google Scholar
Dimitropoulos, C. D., Sureshkumar, R., Beris, A. N. & Handler, R. A. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13, 1016–1027.Google Scholar
Egolf, P. W. 1994 Difference-quotient turbulence model: a generalization of Prandtl’s mixing-length theory. Phys. Rev. E 49, 1260–1268.Google Scholar
Egolf, P. W. 2009 Lévy statistics and beta model: a new solution of ‘wall’ turbulence with a critical phenomenon. Intl J. Refrig. 32, 1815–1836.Google Scholar
Egolf, P. W. & Weiss, D. A. 1998 Difference-quotient turbulence model: the axisymmetric isothermal jet. Phys. Rev. E 58, 459–469.Google Scholar
Gatski, T. B. & Speziale, C. G. 1993 On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254, 59–78.CrossRefGoogle Scholar
Graham, J., Kanov, K., Yang, X. I. A., Lee, M., Malaya, N., Lalescu, C. C., Burns, R., Eyink, G., Szalay, A., Moser, R. D. & Meneveau, C. 2016 A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J. Turbul. 17, 181–215.CrossRefGoogle Scholar
Hamba, F. 2005 Nonlocal analysis of the Reynolds stress in turbulent shear flow. Phys. Fluids 17, 115102.CrossRefGoogle Scholar
Hamba, F. 2013 Exact transport equation for local eddy viscosity in turbulent shear flow. Phys. Fluids 25, 085102.Google Scholar
Handler, R. A., Bernard, P. S., Rovelstad, A. & Swearingen, J. 1992 On the role of accelerating particles in the generation of Reynolds stress. Phys. Fluids A 4, 1317–1319.Google Scholar
Jones, W. P. & Launder, B. E. 1972 The prediction of laminarization with a two-equation model of turbulence. Intl J. Heat Mass Transfer 15, 301–314.Google Scholar
Kays, W. M. & Crawford, M. E. 1993 Convective Heat and Mass Transfer, 3rd edn. McGraw-Hill.Google Scholar
Lesieur, M. & Métais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 45–82.Google Scholar
Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A. & Eyink, G. 2008 A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9, 1–29.Google Scholar
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
Massey, F. J. 1951 The Kolmogorov–Smirnov test for goodness of fit. J. Am. Stat. Assoc. 46, 68–78.Google Scholar
Menter, F. R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 8, 1598–1605.Google Scholar
Perlman, E., Burns, R., Li, Y. & Meneveau, C. 2007 Data exploration of turbulence simulations using a database cluster. In Proceedings of the 2007 ACM/IEEE Conference on Supercomputing, pp. 1–11. ACM.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Prandtl, L. 1925 Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech. 5, 136–139.Google Scholar
Prandtl, L. 1942 Bemerkungen zur Theorie der freien Turbulenz. Z. Angew. Math. Mech. 22, 241–243.CrossRefGoogle Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer.Google Scholar
Schmitt, F. G. 2007 About Boussinesq’s turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. C. R. Mécanique 335, 617–627.Google Scholar
Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1, 5–21.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. 1932 The transport of vorticity and heat through fluids in turbulent motion. Proc. R. Soc. Lond. A 135, 685–705.Google Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.Google Scholar
Wilcox, D. C. 2008 Formulation of the k–𝜔 turbulence model revisited. AIAA J. 46, 2823–2838.Google Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid. Mech. 630, 5–41.CrossRefGoogle Scholar
Yoshizawa, A. 1984 Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation. Phys. Fluids 27, 1377–1387.Google Scholar