Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-20T02:24:47.570Z Has data issue: false hasContentIssue false

An isolated logarithmic layer

Published online by Cambridge University Press:  14 April 2021

Yongseok Kwon*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040Madrid, Spain
Javier Jiménez
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040Madrid, Spain
*
Email address for correspondence: kwon@torroja.dmt.upm.es

Abstract

To isolate the multiscale dynamics of the logarithmic layer of wall-bounded turbulent flows, a novel numerical experiment is conducted in which the mean tangential Reynolds stress is eliminated except in a subregion corresponding to the typical location of the logarithmic layer in channels. Various statistical comparisons against channel flow databases show that, despite some differences, this modified flow system reproduces the kinematics and dynamics of natural logarithmic layers well, even in the absence of a buffer and an outer zone. This supports the previous idea that the logarithmic layer has its own autonomous dynamics. In particular, the results suggest that the mean velocity gradient and the wall-parallel scale of the largest eddies are determined by the height of the tallest momentum-transferring motions, which implies that the very large-scale motions of wall-bounded flows are not an intrinsic part of the logarithmic-layer dynamics. Using a similar set-up, an isolated layer with a constant total stress, which represents the logarithmic layer without a driving force, is simulated and examined.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

del Álamo, J.C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41L44.CrossRefGoogle Scholar
del Álamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.CrossRefGoogle Scholar
del Álamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.CrossRefGoogle Scholar
Bae, H.J. & Lozano-Durán, A. 2019 A minimal flow unit of the logarithmic layer in the absence of near-wall eddies and large scales. In CTR Annual Research Briefs, pp. 1–10. Stanford University.Google Scholar
Balakumar, B.J. & Adrian, R.J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665681.Google ScholarPubMed
Barenblatt, G.I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to $Re_\tau =4000$. J. Fluid Mech. 742, 171191.CrossRefGoogle Scholar
Borrell, G. 2015 Entrainment effects in turbulent boundary layers. PhD thesis, Universidad Politécnica de Madrid.Google Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J. 2017 Coherent structures in statistically stationary homogeneous shear turbulence. J. Fluid Mech. 816, 167208.CrossRefGoogle Scholar
Feldmann, D. & Avila, M. 2018 Overdamped large-eddy simulations of turbulent pipe flow up to $Re_\tau =1500$. J. Phys.: Conf. Ser. 1001, 012016.Google Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22, 071704.CrossRefGoogle Scholar
García-Mayoral, R. & Jiménez, J. 2011 Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317347.CrossRefGoogle Scholar
de Giovanetti, M., Hwang, Y. & Choi, H. 2016 Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511538.CrossRefGoogle Scholar
He, S., He, K. & Seddighi, M. 2016 Laminarisation of flow at low Reynolds number due to streamwise body force. J. Fluid Mech. 809, 3171.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.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647664.Google ScholarPubMed
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254289.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105, 14.CrossRefGoogle ScholarPubMed
Jiménez, J. 1998 The largest scales of turbulent wall flows. In CTR Annual Research Briefs, pp. 943–945. Stanford University.Google Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213240.CrossRefGoogle Scholar
Jiménez, J. & Moser, R.D. 2000 LES: where are we and what can we expect? AIAA J. 38, 605612.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.CrossRefGoogle Scholar
Jiménez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89117.CrossRefGoogle Scholar
Johnstone, R., Coleman, G.N. & Spalart, P.R. 2010 The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation. J. Fluid Mech. 643, 163175.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R.D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.CrossRefGoogle Scholar
Kim, K.C. & Adrian, R.J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417422.CrossRefGoogle Scholar
Kühnen, J., Song, B., Scarselli, D., Budanur, N.B., Riedl, M., Willis, A.P., Avila, M. & Hof, B. 2018 Destabilizing turbulence in pipe flow. Nat. Phys. 14, 386390.CrossRefGoogle Scholar
Kwon, Y.S. 2016 The quiescent core of turbulent channel and pipe flows. PhD thesis, The University of Melbourne.Google Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_\tau \approx 5200$. J. Fluid Mech. 774, 395415.CrossRefGoogle Scholar
Lele, S.K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.CrossRefGoogle Scholar
Lozano-Durán, A. & Bae, H.J. 2019 Characteristic scales of Townsend's wall-attached eddies. J. Fluid Mech. 868, 698725.CrossRefGoogle ScholarPubMed
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100130.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re_\tau =4200$. Phys. Fluids 26, 011702.CrossRefGoogle Scholar
Luchini, P. 2017 Universality of the turbulent velocity profile. Phys. Rev. Lett. 118, 224501.CrossRefGoogle ScholarPubMed
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418428.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.CrossRefGoogle Scholar
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429455.CrossRefGoogle Scholar
Perry, A.E. & Abell, J. 1977 Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes. J. Fluid Mech. 79, 785799.CrossRefGoogle Scholar
Perry, A.E. & Chong, M.S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 137217.CrossRefGoogle Scholar
Pumir, A. 1996 Turbulence in homogeneous shear flows. Phys. Fluids 8, 31123127.CrossRefGoogle Scholar
Russo, S. & Luchini, P. 2016 The linear response of turbulent flow to a volume force: comparison between eddy-viscosity model and DNS. J. Fluid Mech. 790, 104127.CrossRefGoogle Scholar
Sekimoto, A., Dong, S. & Jiménez, J. 2016 Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows. Phys. Fluids 28, 035101.CrossRefGoogle Scholar
Smargorinsky, J. 1963 General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weath. Rev. 91, 99164.2.3.CO;2>CrossRefGoogle Scholar
Spalart, P.R., Moser, R.D. & Rogers, M.M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297324.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Tuerke, F. & Jiménez, J. 2013 Simulations of turbulent channels with prescribed velocity profiles. J. Fluid Mech. 723, 587603.CrossRefGoogle Scholar
Vela-Martín, A., Encinar, M.P., García-Gutiérrez, A. & Jiménez, J. 2019 A second-order consistent, low-storage method for time-resolved channel flow simulations up to $Re_\tau =5300$. In Technical Note ETSIAE/MF-0219, pp. 1–19. Universidad Politécnica de Madrid.Google Scholar