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Self-similarity of turbulent jet flows with internal and external intermittency

Published online by Cambridge University Press:  01 June 2021

M. Gauding ,
M. Bode ,
Y. Brahami ,
É. Varea  and
L. Danaila
M. Gauding*
Affiliation:
CORIA – CNRS UMR 6614, 76801 Saint Etienne du Rouvray, France
M. Bode
Affiliation:
Institute for Combustion Technology, RWTH Aachen University, Aachen, Germany
Y. Brahami
Affiliation:
CORIA – CNRS UMR 6614, 76801 Saint Etienne du Rouvray, France
É. Varea
Affiliation:
CORIA – CNRS UMR 6614, 76801 Saint Etienne du Rouvray, France
L. Danaila
Affiliation:
CORIA – CNRS UMR 6614, 76801 Saint Etienne du Rouvray, France Normandie University, UNIROUEN, UNICAEN, CNRS, M2C, 76000 Rouen, France
*
†Email address for correspondence: michael@gauding.de
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Abstract

The combined effect of internal and external intermittency on the statistical properties of small-scale turbulence is investigated in temporally evolving, planar turbulent jet flows at different Reynolds numbers using highly resolved direct numerical simulations. In turbulent jet flows, the phenomenon of external intermittency originates from a sharp layer, known as the turbulent/non-turbulent interface, that separates the turbulent core from the surrounding irrotational fluid. First, it is shown that low-order and higher-order structure functions in both the core and the shear layer of the jet satisfy complete self-preservation, which means that structure functions are invariant with time and collapse over the entire range of scales, regardless of the set of length and velocity scales used for normalization. Next, the impact of external intermittency on small-scale turbulence is studied along the cross-wise direction by the self-similarity of structure functions. It is shown that structure functions exhibit from the centre toward the edge of the flow a growing departure from self-similarity and the prediction of classical scaling theories. By analysing statistics conditioned on the turbulent portion of the jet, it is demonstrated that this departure is primarily due to external intermittency and the associated similarity-breaking effect.

JFM classification

Turbulent Flows: Intermittency Wakes/Jets: Jets Turbulent Flows: Turbulence simulation

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JFM Papers
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Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A41
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© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anselmet, F., Gagne, Y., Hopfinger, E. & Antonia, R. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.CrossRefGoogle Scholar
Antonia, R.A., Smalley, R., Zhou, T., Anselmet, F. & Danaila, L. 2003 Similarity of energy structure functions in decaying homogeneous isotropic turbulence. J. Fluid Mech. 487, 245–269.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Baudet, C. & Chavarria, G.R. 1995 On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D 80 (4), 385–398.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. A 48 (1), R29–R32.Google ScholarPubMed
Bisset, D.K., Hunt, J.C. & Rogers, M.M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Bode, M., Gauding, M., Lian, Z., Denker, D., Davidovic, M., Kleinheinz, K., Jitsev, J. & Pitsch, H. 2021 Using physics-informed enhanced super-resolution generative adversarial networks for subfilter modeling in turbulent reactive flows. Proc. Combust. Inst. 38 (2), 2617–2625.CrossRefGoogle Scholar
Boschung, J., Hennig, F., Gauding, M., Pitsch, H. & Peters, N. 2016 Generalised higher-order Kolmogorov scales. J. Fluid Mech. 794, 233–251.CrossRefGoogle Scholar
Casciola, C., Gualtieri, P., Benzi, R. & Piva, R. 2003 Scale-by-scale budget and similarity laws for shear turbulence. J. Fluid Mech. 476, 105–114.CrossRefGoogle Scholar
Chien, C.-C., Blum, D.B. & Voth, G.A. 2013 Effects of fluctuating energy input on the small scales in turbulence. J. Fluid Mech. 737, 527–551.CrossRefGoogle Scholar
Corrsin, S. & Kistler, A.L. 1955 Free-stream boundaries of turbulent flows. NACA Tech. Rep. 1244.Google Scholar
Debye, P., Anderson, H.Jr. & Brumberger, H. 1957 Scattering by an inhomogeneous solid. II. The correlation function and its application. J. Appl. Phys. 28 (6), 679–683.CrossRefGoogle Scholar
Debye, P. & Bueche, A. 1949 Scattering by an inhomogeneous solid. J. Appl. Phys. 20 (6), 518–525.CrossRefGoogle Scholar
Denker, D., Attili, A., Boschung, J., Hennig, F., Gauding, M., Bode, M. & Pitsch, H. 2020 Dissipation element analysis of non-premixed jet flames. J. Fluid Mech. 905, A4.CrossRefGoogle Scholar
Djenidi, L., Lefeuvre, N., Kamruzzaman, M. & Antonia, R. 2017 On the normalized dissipation parameter $c_\varepsilon$ in decaying turbulence. J. Fluid Mech. 817, 61–79.CrossRefGoogle Scholar
Elsinga, G. & da Silva, C. 2019 How the turbulent/non-turbulent interface is different from internal turbulence. J. Fluid Mech. 866, 216–238.CrossRefGoogle Scholar
Erlebacher, G., Hussaini, M., Kreiss, H. & Sarkar, S. 1990 The analysis and simulation of compressible turbulence. Theor. Comput. Fluid Dyn. 2 (2), 73–95.Google Scholar
Fitzhugh, R. 1983 Statistical properties of the asymmetric random telegraph signal, with applications to single-channel analysis. Math. Biosci. 64 (1), 75–89.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence - The legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gauding, M., Bode, M., Denker, D., Brahami, Y., Danaila, L. & Varea, E. 2021 On the combined effect of internal and external intermittency in turbulent non-premixed jet flames. Proc. Combust. Inst. 38 (2), 2767–2774.CrossRefGoogle Scholar
Gauding, M., Dietzsch, F., Goebbert, J.H., Thévenin, D., Abdelsamie, A. & Hasse, C. 2017 Dissipation element analysis of a turbulent non-premixed jet flame. Phys. Fluids 29 (8), 085103.CrossRefGoogle Scholar
Gauding, M., Wang, L., Goebbert, J.H., Bode, M., Danaila, L. & Varea, E. 2019 On the self-similarity of line segments in decaying homogeneous isotropic turbulence. Comput. Fluids 180, 206–217.CrossRefGoogle Scholar
Gauding, M., Wick, A., Pitsch, H. & Peters, N. 2014 Generalised scale-by-scale energy-budget equations and large-eddy simulations of anisotropic scalar turbulence at various Schmidt numbers. J. Turbul. 15 (12), 857–882.CrossRefGoogle Scholar
George, W.K. 1992 Self-preservation of temperature fluctuations in isotropic turbulence. In Studies in Turbulence, pp. 514–528. Springer.CrossRefGoogle Scholar
George, W.K. 2009 Is there an asymptotic effect of initial and upstream conditions on turbulence? In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences, pp. 647–672. American Society of Mechanical Engineers Digital Collection.Google Scholar
Gonzalez, M. & Fall, A. 1998 The approach to self-preservation of scalar fluctuations decay in isotropic turbulence. Phys. Fluids 10 (3), 654–661.CrossRefGoogle Scholar
Gotoh, T., Fukayama, D. & Nakano, T. 2002 Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Phys. Fluids 14 (3), 1065–1081.CrossRefGoogle Scholar
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., 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
Hunger, F., Gauding, M. & Hasse, C. 2016 On the impact of the turbulent/non-turbulent interface on differential diffusion in a turbulent jet flow. J. Fluid Mech. 802, R5.CrossRefGoogle Scholar
Iyer, K.P., Sreenivasan, K.R. & Yeung, P. 2020 Scaling exponents saturate in three-dimensional isotropic turbulence. Phys. Rev. Fluids 5 (5), 054605.CrossRefGoogle Scholar
von Kármán, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164 (917), 192–215.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.Google Scholar
Kolmogorov, A.N. 1941 b The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kolmogorov, A.N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13 (1), 82–85.CrossRefGoogle Scholar
Kraichnan, R.H. 1974 On Kolmogorov's inertial-range theories. J. Fluid Mech. 62 (2), 305–330.CrossRefGoogle Scholar
Krug, D., Chung, D., Philip, J. & Marusic, I. 2017 a Global and local aspects of entrainment in temporal plumes. J. Fluid Mech. 812, 222–250.CrossRefGoogle Scholar
Krug, D., Holzner, M., Marusic, I. & van Reeuwijk, M. 2017 b Fractal scaling of the turbulence interface in gravity currents. J. Fluid Mech. 820, R3.CrossRefGoogle Scholar
Kuznetsov, V., Praskovsky, A. & Sabelnikov, V. 1992 Fine-scale turbulence structure of intermittent hear flows. J. Fluid Mech. 243, 595–622.CrossRefGoogle Scholar
Landau, L. & Lifshitz, E. 1963 Fluid mechanics.Google Scholar
Lawson, J.M., Bodenschatz, E., Knutsen, A.N., Dawson, J.R. & Worth, N.A. 2019 Direct assessment of Kolmogorov's first refined similarity hypothesis. Phys. Rev. Fluids 4 (2), 022601.CrossRefGoogle Scholar
Lele, S.K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle Scholar
Maurer, J., Tabeling, P. & Zocchi, G. 1994 Statistics of turbulence between two counterrotating disks in low-temperature helium gas. Europhys. Lett. 26 (1), 31.CrossRefGoogle Scholar
Meldi, M. & Sagaut, P. 2013 Further insights into self-similarity and self-preservation in freely decaying isotropic turbulence. J. Turbul. 14 (8), 24–53.CrossRefGoogle Scholar
Mellado, J.P. & Ansorge, C. 2012 Factorization of the fourier transform of the pressure-poisson equation using finite differences in colocated grids. Z. Angew. Math. Mech. 92 (5), 380–392.CrossRefGoogle Scholar
Mellado, J.P., Stevens, B., Schmidt, H. & Peters, N. 2010 Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation. Theor. Comput. Fluid Dyn. 24 (6), 511–536.CrossRefGoogle Scholar
Mellado, J.P., Wang, L. & Peters, N. 2009 Gradient trajectory analysis of a scalar field with external intermittency. J. Fluid Mech. 626, 333–365.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.CrossRefGoogle Scholar
Mi, J. & Antonia, R. 2001 Effect of large-scale intermittency and mean shear on scaling-range exponents in a turbulent jet. Phys. Rev. E 64 (2), 026302.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331–368.CrossRefGoogle Scholar
Nelkin, M. 1994 Universality and scaling in fully developed turbulence. Adv. Phys. 43 (2), 143–181.CrossRefGoogle Scholar
Obukhov, A. 1962 Some specific features of atmospheric turbulence. J. Fluid Mech. 13 (1), 77–81.CrossRefGoogle Scholar
Pearson, B. & Antonia, R. 2001 Reynolds-number dependence of turbulent velocity and pressure increments. J. Fluid Mech. 444, 343–382.CrossRefGoogle Scholar
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254–275.CrossRefGoogle Scholar
Sabelnikov, V., Lipatnikov, A.N., Nishiki, S. & Hasegawa, T. 2019 Investigation of the influence of combustion-induced thermal expansion on two-point turbulence statistics using conditioned structure functions. J. Fluid Mech. 867, 45–76.CrossRefGoogle Scholar
Sadeghi, H., Lavoie, P. & Pollard, A. 2015 Equilibrium similarity solution of the turbulent transport equation along the centreline of a round jet. J. Fluid Mech. 772, 740–755.CrossRefGoogle Scholar
Sadeghi, H., Oberlack, M. & Gauding, M. 2018 On new scaling laws in a temporally evolving turbulent plane jet using lie symmetry analysis and direct numerical simulation. J. Fluid Mech. 854, 233–260.CrossRefGoogle Scholar
Saffman, P. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27 (3), 581–593.CrossRefGoogle Scholar
Schumacher, J., Scheel, J.D., Krasnov, D., Donzis, D.A., Yakhot, V. & Sreenivasan, K.R. 2014 Small-scale universality in fluid turbulence. Proc. Natl Acad. Sci. 111 (30), 10961–10965.CrossRefGoogle ScholarPubMed
da Silva, C.B., Hunt, J.C., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567–590.CrossRefGoogle Scholar
da Silva, C.B. & Pereira, J.C. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20 (5), 055101.CrossRefGoogle Scholar
de Silva, C.M., Krug, D., Lohse, D. & Marusic, I. 2017 Universality of the energy-containing structures in wall-bounded turbulence. J. Fluid Mech. 823, 498–510.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
Sinhuber, M., Bodenschatz, E. & Bewley, G.P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114 (3), 034501.CrossRefGoogle ScholarPubMed
Speziale, C.G. & Bernard, P.S. 1992 The energy decay in self-preserving isotropic turbulence revisited. J. Fluid Mech. 241, 645–667.CrossRefGoogle Scholar
Sreenivasan, K.R. & Antonia, R. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435–472.CrossRefGoogle Scholar
Stephan, M. & Docter, J. 2015 JUQUEEN: IBM Blue Gene/Q supercomputer system at the Jülich supercomputing centre. JLSRF 1, 1.CrossRefGoogle Scholar
Tang, S., Antonia, R., Djenidi, L., Danaila, L. & Zhou, Y. 2017 Finite Reynolds number effect on the scaling range behaviour of turbulent longitudinal velocity structure functions. J. Fluid Mech. 820, 341–369.CrossRefGoogle Scholar
Tang, S., Antonia, R., Djenidi, L. & Zhou, Y. 2016 Complete self-preservation along the axis of a circular cylinder far wake. J. Fluid Mech. 786, 253–274.CrossRefGoogle Scholar
Thiesset, F., Antonia, R. & Danaila, L. 2013 a Restricted scaling range models for turbulent velocity and scalar energy transfers in decaying turbulence. J. Turbul. 14 (3), 25–41.CrossRefGoogle Scholar
Thiesset, F., Antonia, R. & Djenidi, L. 2014 a Consequences of self-preservation on the axis of a turbulent round jet. J. Fluid Mech. 748, R2.CrossRefGoogle Scholar
Thiesset, F., Danaila, L. & Antonia, R. 2013 b Dynamical effect of the total strain induced by the coherent motion on local isotropy in a wake. J. Fluid Mech. 720, 393–423.CrossRefGoogle Scholar
Thiesset, F., Duret, B., Ménard, T., Dumouchel, C., Reveillon, J. & Demoulin, F.X. 2020 Liquid transport in scale space. J. Fluid Mech. 886, A4.CrossRefGoogle Scholar
Thiesset, F., Schaeffer, V., Djenidi, L. & Antonia, R. 2014 b On self-preservation and log-similarity in a slightly heated axisymmetric mixing layer. Phys. Fluids 26 (7), 075106.CrossRefGoogle Scholar
Townsend, A. 1949 The fully developed wake of a circular cylinder. Aust. J. Chem. 2 (4), 451–468.CrossRefGoogle Scholar
Townsend, A. 1951 On the fine-scale structure of turbulence. Proc. R. Soc. Lond. A 208 (1095), 534–542.Google Scholar
Watanabe, T. & Gotoh, T. 2007 Inertial-range intermittency and accuracy of direct numerical simulation for turbulence and passive scalar turbulence. J. Fluid Mech. 590, 117–146.CrossRefGoogle Scholar
Watanabe, T., da Silva, C. & Nagata, K. 2020 Scale-by-scale kinetic energy budget near the turbulent/nonturbulent interface. Phys. Rev. Fluids 5 (12), 124610.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
Westerweel, J., Fukushima, C., Pedersen, J.M. & Hunt, J. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.CrossRefGoogle Scholar
Yasuda, T. & Vassilicos, J.C. 2018 Spatio-temporal intermittency of the turbulent energy cascade. J. Fluid Mech. 853, 235–252.CrossRefGoogle Scholar
Zhou, Y. & Vassilicos, J. 2020 Energy cascade at the turbulent/nonturbulent interface. Phys. Rev. Fluids 5 (6), 064604.CrossRefGoogle Scholar