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Simulations of turbulent channels with prescribed velocity profiles

Published online by Cambridge University Press:  16 April 2013

Florian Tuerke  and
Javier Jiménez
Florian Tuerke
Affiliation:
Institut für Strömungsmechanik und Akustik, Technische Universität Berlin, Müller-Breslau-Strasse 8, 10623 Berlin, Germany School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Javier Jiménez*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain Centre for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations of turbulent channels with artificially prescribed velocity profiles are discussed, using both natural and purposely incorrect profiles. It is found that turbulence develops correctly when natural profiles are prescribed, but that even slightly incorrect ones modify the Reynolds stresses substantially. That is used to study the dynamics of the energy-containing velocity fluctuations. The stronger (weaker) structures generated by locally stronger (weaker) mean shears have essentially correct isotropy coefficients but they are out of energy equilibrium, with the energy imbalance compensated by turbulent diffusion. The velocity scale in smooth profiles changes with the distance to the wall, and is best described by a friction velocity derived from the local total tangential stress. The behaviour across sharper shear jumps is more consistent with non-equilibrium eddies that relax over wall-normal distances of the order of the distance to the wall, suggesting that the energy equilibrium in the logarithmic layer is not local to a given height, but applies to extended layers homogenized by wall-normal fluxes. Examples of that non-local character are the large-scale inactive fluctuations near the wall, whose velocities do not scale with the local shear stress, but with that of their active ‘cores’ farther away from the wall.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 587 - 603
Copyright
©2013 Cambridge University Press 

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Footnotes

‡

Present address: Laboratorio de Fluidodinámica, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, C1063ACV Buenos Aires, Argentina.

References

del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Bradshaw, P. 1967 Inactive motions and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241–258.Google Scholar
Cess, R. D. 1958 A survey of the literature on heat transfer in turbulent tube flow. Report 8-0529-R24. Westinghouse Research.Google Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22, 071704.Google Scholar
deGraaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to ${Re}_{\tau } = 2003$ . Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108, 094501.Google Scholar
Jarrin, N. 2007 Synthetic inflow boundary conditions for numerical simulation of turbulent flow. PhD thesis, Engineering and Phys. Sci., University of Manchester.Google Scholar
Jiménez, J. 1993 Energy transfer and constrained simulations in isotropic turbulence. In CTR Annu. Res. Briefs, pp. 171–186. Stanford University.Google Scholar
Jiménez, J. 2010 Wall turbulence with arbitrary mean velocity profiles. In CTR Annu. Res. Briefs, pp. 17–24. Stanford University.Google Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.Google Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 389, 335–359.Google Scholar
Kerr, R. M. 1990 Velocity, scalar and transfer spectra in numerical turbulence. J. Fluid Mech. 211, 309–332.Google Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluids a very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.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
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13, 692–701.CrossRefGoogle Scholar
Mizuno, Y. & Jiménez, J. 2011 Mean velocity and length scales in the overlap region of wall-bounded turbulent flows. Phys. Fluids 23, 085112.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of a turbulent channel flow up to ${Re}_{\tau } = 590$ . Phys. Fluids 11, 943–945.Google Scholar
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. 2006 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755–770.Google Scholar
Obukhov, A. M. 1941 On the distribution of energy in the spectrum of turbulent flow. Dokl. Akad. Nauk SSSR 32, 22–24.Google Scholar
Perry, A. E. & Abell, C. J. 1975 Scaling laws for pipe-flow turbulence. J. Fluid Mech. 67, 257–271.Google Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Perry, A. E. & Li, J. D. 1990 Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405–438.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
She, Z.-S. & Jackson, E. 1993 Constrained Euler system for Navier–Stokes turbulence. Phys. Rev. Lett. 70, 1255–1258.Google Scholar
Shtilman, L. & Chasnov, J. R. 1992 LES versus DNS: a comparative study. In Proc. CTR Summer School, pp. 137–143. Stanford University.Google Scholar
Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228, 4218–4231.Google Scholar
Smits, A. J., MacKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.Google Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral method for the Navier–Stokes equations with one infinite and two periodic dimensions. J. Comput. Phys. 96, 297–324.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Tuerke, F. 2011 An inverse RANS simulation of a turbulent channel flow at moderate Reynolds numbers. Master thesis, Universidad Politécnica Madrid.Google Scholar
Zhou, Y. 1993 Interacting scales and energy transfer in isotropic turbulence. Phys. Fluids A 5, 2511–2524.Google Scholar