×

An isolated logarithmic layer. (English) Zbl 1461.76275

Summary: 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.

MSC:

76F40 Turbulent boundary layers
76F10 Shear flows and turbulence
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Del Álamo, J.C. & Jiménez, J.2003Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids15, L41-L44. · Zbl 1186.76136
[2] Del Álamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D.2004Scaling of the energy spectra of turbulent channels. J. Fluid Mech.500, 135-144. · Zbl 1059.76031
[3] Del Álamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D.2006Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech.561, 329-358. · Zbl 1157.76346
[4] 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.
[5] Balakumar, B.J. & Adrian, R.J.2007Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A365, 665-681. · Zbl 1152.76369
[6] Barenblatt, G.I.1996Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press. · Zbl 0907.76002
[7] Bernardini, M., Pirozzoli, S. & Orlandi, P.2014Velocity statistics in turbulent channel flow up to \(Re_\tau =4000\). J. Fluid Mech.742, 171-191.
[8] Borrell, G.2015 Entrainment effects in turbulent boundary layers. PhD thesis, Universidad Politécnica de Madrid.
[9] Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J.2017Coherent structures in statistically stationary homogeneous shear turbulence. J. Fluid Mech.816, 167-208. · Zbl 1383.76181
[10] Feldmann, D. & Avila, M.2018Overdamped large-eddy simulations of turbulent pipe flow up to \(Re_\tau =1500\). J. Phys.: Conf. Ser.1001, 012016.
[11] Flores, O. & Jiménez, J.2010Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids22, 071704.
[12] García-Mayoral, R. & Jiménez, J.2011Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech.678, 317-347. · Zbl 1241.76175
[13] De Giovanetti, M., Hwang, Y. & Choi, H.2016Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech.808, 511-538. · Zbl 1383.76256
[14] He, S., He, K. & Seddighi, M.2016Laminarisation of flow at low Reynolds number due to streamwise body force. J. Fluid Mech.809, 31-71. · Zbl 1383.76228
[15] Hoyas, S. & Jiménez, J.2006Scaling of the velocity fluctuations in turbulent channels up to \(Re_\tau =2003\). Phys. Fluids18, 011702.
[16] Hoyas, S. & Jiménez, J.2008Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids20, 101511. · Zbl 1182.76330
[17] Hutchins, N. & Marusic, I.2007Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A365, 647-664. · Zbl 1152.76421
[18] Hwang, Y.2015Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech.767, 254-289.
[19] Hwang, Y. & Cossu, C.2010Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett.105, 1-4.
[20] Jiménez, J.1998 The largest scales of turbulent wall flows. In CTR Annual Research Briefs, pp. 943-945. Stanford University.
[21] Jiménez, J.2018Coherent structures in wall-bounded turbulence. J. Fluid Mech.842, P1. · Zbl 1419.76316
[22] Jiménez, J. & Moin, P.1991The minimal flow unit in near-wall turbulence. J. Fluid Mech.225, 213-240. · Zbl 0721.76040
[23] Jiménez, J. & Moser, R.D.2000LES: where are we and what can we expect?AIAA J.38, 605-612.
[24] Jiménez, J. & Pinelli, A.1999The autonomous cycle of near-wall turbulence. J. Fluid Mech.389, 335-359. · Zbl 0948.76025
[25] Jiménez, J., Uhlmann, M., Pinelli, A. & Kawahara, G.2001Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech.442, 89-117. · Zbl 1014.76027
[26] Johnstone, R., Coleman, G.N. & Spalart, P.R.2010The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation. J. Fluid Mech.643, 163-175. · Zbl 1189.76264
[27] Kim, J., Moin, P. & Moser, R.D.1987Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech.177, 133-166. · Zbl 0616.76071
[28] Kim, K.C. & Adrian, R.J.1999Very large-scale motion in the outer layer. Phys. Fluids11, 417-422. · Zbl 1147.76430
[29] Kühnen, J., Song, B., Scarselli, D., Budanur, N.B., Riedl, M., Willis, A.P., Avila, M. & Hof, B.2018Destabilizing turbulence in pipe flow. Nat. Phys.14, 386-390.
[30] Kwon, Y.S.2016 The quiescent core of turbulent channel and pipe flows. PhD thesis, The University of Melbourne.
[31] Lee, M. & Moser, R.D.2015Direct numerical simulation of turbulent channel flow up to \(Re_\tau \approx 5200\). J. Fluid Mech.774, 395-415.
[32] Lele, S.K.1992Compact finite difference schemes with spectral-like resolution. J. Comput. Phys.103, 16-42. · Zbl 0759.65006
[33] Lozano-Durán, A. & Bae, H.J.2019Characteristic scales of Townsend’s wall-attached eddies. J. Fluid Mech.868, 698-725. · Zbl 1415.76351
[34] Lozano-Durán, A., Flores, O. & Jiménez, J.2012The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech.694, 100-130. · Zbl 1250.76108
[35] Lozano-Durán, A. & Jiménez, J.2014Effect of the computational domain on direct simulations of turbulent channels up to \(Re_\tau =4200\). Phys. Fluids26, 011702.
[36] Luchini, P.2017Universality of the turbulent velocity profile. Phys. Rev. Lett.118, 224501. · Zbl 1408.76338
[37] Marusic, I., Mathis, R. & Hutchins, N.2010High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow31, 418-428.
[38] Mizuno, Y. & Jiménez, J.2011Mean velocity and length-scales in the overlap region of wall-bounded turbulent flows. Phys. Fluids23, 085112.
[39] Mizuno, Y. & Jiménez, J.2013Wall turbulence without walls. J. Fluid Mech.723, 429-455. · Zbl 1287.76137
[40] Perry, A.E. & Abell, J.1977Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes. J. Fluid Mech.79, 785-799.
[41] Perry, A.E. & Chong, M.S.1982On the mechanism of wall turbulence. J. Fluid Mech.119, 137-217. · Zbl 0517.76057
[42] Pumir, A.1996Turbulence in homogeneous shear flows. Phys. Fluids8, 3112-3127. · Zbl 1027.76582
[43] Russo, S. & Luchini, P.2016The linear response of turbulent flow to a volume force: comparison between eddy-viscosity model and DNS. J. Fluid Mech.790, 104-127. · Zbl 1382.76144
[44] Sekimoto, A., Dong, S. & Jiménez, J.2016Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows. Phys. Fluids28, 035101.
[45] Smargorinsky, J.1963General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weath. Rev.91, 99-164.
[46] Spalart, P.R., Moser, R.D. & Rogers, M.M.1991Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys.96, 297-324. · Zbl 0726.76074
[47] Townsend, A.A.1976The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press. · Zbl 0325.76063
[48] Tuerke, F. & Jiménez, J.2013Simulations of turbulent channels with prescribed velocity profiles. J. Fluid Mech.723, 587-603. · Zbl 1287.76140
[49] 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.