Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-07T16:48:27.243Z Has data issue: false hasContentIssue false
  • English
  • Français

Universality of small-scale motions within the turbulent/non-turbulent interface layer

Published online by Cambridge University Press:  06 April 2021

Marco Zecchetto Open the ORCID record for Marco Zecchetto [Opens in a new window]  and
Carlos B. da Silva Open the ORCID record for Carlos B. da Silva [Opens in a new window]
Marco Zecchetto
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
Carlos B. da Silva*
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The universality of the statistics of small-scale motions within the turbulent/non-turbulent interface (TNTI) layer that exists at the edges of turbulent free shear flows (i.e. mixing layers) and in turbulent boundary layers is analysed using direct numerical simulations of turbulent jets, wakes and in turbulent fronts evolving without mean shear. The Taylor based Reynolds number of the simulations is $Re_{\lambda } \gtrsim 200$ while the resolution is comparable to the Kolmogorov micro-scale ${\rm \Delta} x \approx \eta$. It is shown that, when properly normalised by using the local Kolmogorov velocity and length scales, the statistics of the vorticity, strain and related quantities, such as the invariants of the velocity gradient tensor, are universal, i.e. virtually equal for the same position within the TNTI layer, which implies the universality of the small-scale ‘nibbling’ associated with the turbulent entrainment mechanism. The results show that the small scales of motion near the TNTI layer are statistically very close to homogeneous, except for a distance of about 10 Kolmogorov micro-scales from the outer surface of the TNTI layer. The proposed normalisation allows for a much more clear identification of the viscous superlayer and the turbulent sublayer within the TNTI layer.

JFM classification

Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A9
Check for updates
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

Alvelius, K. 1999 Random forcing of three-dimensional homogeneous turbulence. Phys. Fluids 11 (7), 1880–1889.CrossRefGoogle Scholar
Attili, A., Cristancho, J.C. & Bisetti, F. 2014 Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer. J. Turbul. 15, 555–568.CrossRefGoogle Scholar
Bisset, D.K., Hunt, J.C.R. & Rogers, M.M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Blackburn, H., Mansour, N. & Cantwell, B. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292.CrossRefGoogle Scholar
Borrell, G. & Jiménez, J. 2016 Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 801, 554–596.CrossRefGoogle Scholar
Breda, M. & Buxton, O.R.H. 2019 Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets. J. Fluid Mech. 879, 187–216.CrossRefGoogle Scholar
Cantwell, B. 1993 On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence. Phys. Fluids 5 (8), 2008–2013.CrossRefGoogle Scholar
Canuto, C., Hussaini, M.Y., Quarteroni, A. & Zang, T.A. 1987 Spectral Methods in Fluid Dynamics. Springer-Verlag.Google Scholar
Chauhan, K., Philip, J. & Marusic, I. 2014 a Scaling of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 751, 1–31.CrossRefGoogle Scholar
Chauhan, K., Philip, J., de Silva, C.M., Hutchins, N. & Marusic, I. 2014 b The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151.CrossRefGoogle Scholar
Chong, M.S., Soria, J., Perry, A.E., Chacin, J., Cantwell, B.J. & Na, Y. 1998 Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247.CrossRefGoogle Scholar
Cimarelli, A., Cocconi, G., Frohnapfel, B. & Angelis, E.D. 2015 Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface. Phys. Fluids 27, 125106.CrossRefGoogle Scholar
Corrsin, S. & Kistler, A.L. 1955 Free-stream boundaries of turbulent flows. Tech. Rep. TN-1244. Neighborhood Assistance Corporation of America. pp. 1033–1064.Google Scholar
Davidson, P.A. 2004 Turbulence, An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Donzis, D.A. & Sreenivasan, K.R. 2010 The bottleneck effect and the Kolmogorov constant in isotropic turbulence. J. Fluid Mech. 657, 171–188.CrossRefGoogle Scholar
Elsinga, G. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.CrossRefGoogle Scholar
George, W.K. 1989 The self-preservation of turbulent flows and its relation to initial conditions and coherent structures. In Advances in Turbulence (ed. R. Arndt & W.K. George), pp. 39–73. Hemisphere.Google Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J.C. 2014 Evolution of the velocity-gradient tensor in a spatially developing turbulent flow. J. Fluid Mech. 756, 252–292.CrossRefGoogle Scholar
Guimarães, M.C., Pimentel, N., Pinho, F.T. & da Silva, C.B. 2020 Direct numerical simulations of turbulent viscoelastic jets. J. Fluid Mech. 899, 11–37.CrossRefGoogle Scholar
Holzner, M., Liberzon, A., Luthi, B., Nikitin, N., Kinzelbach, W. & Tsinober, A. 2008 A lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465–475.CrossRefGoogle Scholar
Holzner, M., Liberzon, A., Nikitin, N., Kinzelbach, W. & Tsinober, A. 2007 Small-scale aspects of flows in proximity of the turbulent/nonturbulent interface. Phys. Fluids 19, 071702.CrossRefGoogle Scholar
Holzner, M. & Luthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106, 134503.CrossRefGoogle ScholarPubMed
Holzner, M., Luthi, B., Tsinober, A. & Kinzelbach, W. 2009 Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface. J. Fluid Mech. 639, 153–165.CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2007 Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335–366.CrossRefGoogle Scholar
Ishihara, T., Ogasawara, H. & Hunt, J.C.R. 2015 Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers. J. Fluids Struct. 53, 50–57.CrossRefGoogle Scholar
Jahanbakhshi, R. & Madnia, C.K. 2016 Entrainment in a compressible turbulent shear layer. J. Fluid Mech. 797, 564–603.CrossRefGoogle Scholar
Jahanbakhshi, R. & Madnia, C.K. 2018 The effect of heat release on the entrainment in a turbulent mixing layer. J. Fluid Mech. 844, 92–126.CrossRefGoogle Scholar
Lesieur, M., Ossia, S. & Métais, O. 1999 Infrared pressure spectra in 3D and 2D isotropic incompressible turbulence. Phys. Fluids 11, 1535–1543.CrossRefGoogle Scholar
Mistry, D., Philip, J. & Dawson, J.R. 2019 Kinematics of local entrainment and detrainment in a turbulent jet. J. Fluid Mech. 871, 896–924.CrossRefGoogle Scholar
Moser, R.D., Rogers, M.M. & Ewing, D.W. 1998 Self-similarity of time-evolving plane wakes. J. Fluid Mech. 367, 255–289.CrossRefGoogle Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.CrossRefGoogle Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199–227.CrossRefGoogle Scholar
Pope, S.B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ramaprian, B.R., Kalale, K.P.L., Jovic, S. & Kaushik, S. 1984 Study of large-scale mixing in developing wakes behind streamlined bodies. Tech. Rep. CR-173478. National Aeronautics and Space Administration.Google Scholar
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254–275.CrossRefGoogle Scholar
Rogers, M.M. & Moser, R.D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6 (2), 903–923.CrossRefGoogle Scholar
da Silva, C.B., Hunt, J.C.R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulent intensity. Annu. Rev. Fluid Mech. 46, 567–590.CrossRefGoogle Scholar
da Silva, C.B., Lopes, D.C. & Raman, V. 2015 The effect of subgrid-scale models on the entrainment of a passive scalar in a turbulent planar jet. J. Turbul. 16 (4), 342–366.CrossRefGoogle Scholar
da Silva, C.B. & Pereira, J.C.F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.CrossRefGoogle Scholar
da Silva, C.B. & Pereira, J.C.F. 2009 Erratum: ‘invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets’ [Phys. Fluids, 20, 055101, 2008]. Phys. Fluids 21, 019902.CrossRefGoogle Scholar
da Silva, C.B., dos Reis, R.J.N. & Pereira, J.C.F. 2011 The intense vorticity structures near the turbulent/non-turbulent interface a jet. J. Fluid Mech. 685, 165–190.CrossRefGoogle Scholar
Silva, T.S. & da Silva, C.B. 2017 The behaviour of the scalar gradient across the turbulent/non-turbulent interface in jets. Phys. Fluids 29, 085106.CrossRefGoogle Scholar
da Silva, C.B. & Taveira, R.R. 2010 The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys. Fluids 22, 121702.CrossRefGoogle Scholar
Silva, T.S., Zecchetto, M. & da Silva, C.B. 2018 The scaling of the turbulent/non-turbulent interface at high reynolds numbers. J. Fluid Mech. 843, 156–179.CrossRefGoogle Scholar
Soria, J., Sondergaard, R., Cantwell, B., Chong, M. & Perry, A. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6 (2), 871–884.CrossRefGoogle Scholar
Stanley, S., Sarkar, S. & Mellado, J.P. 2002 A study of the flowfield evolution and mixing in a planar turbulent jet using direct numerical simulation. J. Fluid Mech. 450, 377–407.CrossRefGoogle Scholar
Taveira, R.R., Diogo, J.S., Lopes, D.C. & da Silva, C.B. 2013 Lagrangian statistics across the turbulent-nonturbulent interface in a turbulent plane jet. Phys. Rev. E 88, 043001.CrossRefGoogle Scholar
Taveira, R.R. & da Silva, C.B. 2013 Kinetic energy budgets near the turbulent/nonturbulent interface in jets. Phys. Fluids 25, 015114.CrossRefGoogle Scholar
Taveira, R.R. & da Silva, C.B. 2014 Characteristics of the viscous superlayer in free shear turbulence and in planar turbulent jets. Phys. Fluids 26, 021702.CrossRefGoogle Scholar
Teixeira, M.A.C. & da Silva, C.B. 2012 Turbulence dynamics near a turbulent/non-turbulent interface. J. Fluid Mech. 695, 257–287.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tsinober, A. 2019 The Essence of Turbulence as a Physical Phenomenon. Kluwer Academic Publishers.CrossRefGoogle Scholar
Tsinober, A., Ortenberg, M. & Shtilman, L. 1999 On depression of nonlinearity in turbulence. Phys. Fluids 11 (8), 2291–2297.CrossRefGoogle Scholar
Vaghefi, N.S. & Madnia, C.K. 2015 Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 67–94.CrossRefGoogle Scholar
Watanabe, T., Jaulino, R., Taveira, R., da Silva, C.B., Nagata, K. & Sakai, Y. 2017 a Role of an isolated eddy near the turbulent/non-turbulent interface layer. Phys. Rev. Fluids 2, 094607.CrossRefGoogle Scholar
Watanabe, T., Nagata, K. & da Silva, C.B. 2017 b Vorticity evolution near the turbulent/non-turbulent interfaces in free-shear flows. In Vortex Structures in Fluid Dynamic Problems (ed. Dr. H. Perez-De-Tejada), pp. 1–18. InTech.CrossRefGoogle Scholar
Watanabe, T., Riley, J.J., de Bruyn Kops, S.M., Diamessis, P.J. & Zhou, Q. 2016 a Turbulent/non-turbulent interfaces in wakes in stably stratified fluids. J. Fluid Mech. 797, 1–11.CrossRefGoogle Scholar
Watanabe, T., Riley, J.J. & Nagata, K. 2017 c Turbulent entrainment across turbulent-nonturbulent interfaces in stably stratified mixing layers. Phys. Rev. Fluids 2 (10), 104803–104823.CrossRefGoogle Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26, 105103.CrossRefGoogle Scholar
Watanabe, T., da Silva, C.B. & Nagata, K. 2019 Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence. J. Fluid Mech. 875, 321–344.CrossRefGoogle Scholar
Watanabe, T., da Silva, C.B., Sakai, Y., Nagata, K. & Hayase, T. 2016 b Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers. Phys. Fluids 28, 031701.CrossRefGoogle Scholar
Watanabe, T., Zhang, X. & Nagata, K. 2018 Turbulent/non-turbulent interfaces detected in DNS of incompressible turbulent boundary layers. Phys. Fluids 30 (3), 035102.CrossRefGoogle Scholar
Westerweel, J., Fukushima, C., Pedersen, J.M. & Hunt, J.C.R. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95, 174501.CrossRefGoogle ScholarPubMed
Westerweel, J., Fukushima, C., Pedersen, J.M. & Hunt, J.C.R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.CrossRefGoogle Scholar
Westerweel, J., Hofmann, T., Fukushima, C. & Hunt, J.C.R. 2002 The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exp. Fluids 33, 873.CrossRefGoogle Scholar
Weygandt, J.H. & Mehta, R.D. 1995 Three-dimensional structure of straight and curved plane wakes. J. Fluid Mech. 282, 279–311.CrossRefGoogle Scholar
Williamson, J.H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56.CrossRefGoogle Scholar
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J. Fluid Mech. 168, 31–71.CrossRefGoogle Scholar
Zhou, Y. & Antonia, R.A. 1995 Memory effects in a turbulent plane wake. Exp. Fluids 19 (2), 112–120.CrossRefGoogle Scholar