Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-16T02:32:35.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Characteristics of small-scale shear layers in a temporally evolving turbulent planar jet

Published online by Cambridge University Press:  14 June 2021

Masato Hayashi ,
Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window]  and
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]
Masato Hayashi
Affiliation:
Department of Mechanical Systems Engineering, Nagoya University, Nagoya464-8603, Japan
Tomoaki Watanabe*
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya464-8603, Japan
Koji Nagata
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya464-8603, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Characteristics of small-scale shear layers are studied with direct numerical simulations of a temporally evolving turbulent planar jet. The shear layers that internally exist in turbulence are detected with a tensor of shearing motion, which is extracted from a velocity gradient tensor with a triple decomposition. Flow visualization of the shear intensity confirms the existence of layer structures with intense shear. The mean flow characteristics around local maxima of the shear intensity are investigated with averages taken in the shear coordinate system, which is defined based on the shear orientation. The mean flow pattern reveals that the shear layer is formed in a biaxial strain field, which consists of extensive strain in the vorticity direction of the shear and compressive strain in the direction perpendicular to the shear layer. The velocity components associated with the shear and biaxial strain rapidly change around the shear layer. The Kolmogorov scales characterize the mean characteristics of shear layers, such as velocity jumps, thickness and the intensities of shear and biaxial strain. These quantities normalized by the Kolmogorov scales only weakly depend on lateral positions in the planar jet. Although the turbulent planar jet evolves under the influence of mean shear, a large number of the shear layers do not align with the mean shear direction. The typical shear layer thickness is about six times the Kolmogorov length scale. Furthermore, the shear layer thickness is well predicted by the Burgers vortex layer.

JFM classification

Wakes/Jets: Jets Wakes/Jets: Shear layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A38
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

Attili, A., Cristancho, J.C. & Bisetti, F. 2014 Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer. J. Turbul. 15 (9), 555–568.CrossRefGoogle Scholar
Balaras, E., Piomelli, U.G.O. & Wallace, J.M. 2001 Self-similar states in turbulent mixing layers. J. Fluid Mech. 446, 1–24.CrossRefGoogle Scholar
Beronov, K.N. & Kida, S. 1996 Linear two-dimensional stability of a Burgers vortex layer. Phys. Fluids 8 (4), 1024–1035.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
Cafiero, G. & Vassilicos, J.C. 2020 Non-equilibrium scaling of the turbulent-nonturbulent interface speed in planar jets. Phys. Rev. Lett. 125 (17), 174501.CrossRefGoogle Scholar
Davidson, P.A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Deo, R.C., Mi, J. & Nathan, G.J. 2008 The influence of Reynolds number on a plane jet. Phys. Fluids 20 (7), 075108.CrossRefGoogle Scholar
Deo, R.C., Nathan, G.J. & Mi, J. 2013 Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers. Phys. Fluids 25 (1), 015115.CrossRefGoogle Scholar
Diamessis, P.J., Spedding, G.R. & Domaradzki, J.A. 2011 Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes. J. Fluid Mech. 671, 52–95.CrossRefGoogle Scholar
Eisma, J., Westerweel, J., Ooms, G. & Elsinga, G.E. 2015 Interfaces and internal layers in a turbulent boundary layer. Phys. Fluids 27 (5), 055103.CrossRefGoogle Scholar
Elsinga, G.E. & da Silva, C.B. 2019 How the turbulent/non-turbulent interface is different from internal turbulence. J. Fluid Mech. 866, 216–238.CrossRefGoogle Scholar
Gampert, M., Boschung, J., Hennig, F., Gauding, M. & Peters, N. 2014 The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface. J. Fluid Mech. 750, 578–596.CrossRefGoogle Scholar
Ghanem, A., Lemenand, T., Della Valle, D. & Peerhossaini, H. 2014 Static mixers: mechanisms, applications, and characterization methods–a review. Chem. Engng Res. Des. 92 (2), 205–228.CrossRefGoogle Scholar
Gul, M., Elsinga, G.E. & Westerweel, J. 2020 Internal shear layers and edges of uniform momentum zones in a turbulent pipe flow. J. Fluid Mech. 901, A10.CrossRefGoogle Scholar
Gutmark, E. & Wygnanski, I. 1976 The planar turbulent jet. J. Fluid Mech. 73, 465–495.CrossRefGoogle Scholar
Horiuti, K. 2001 A classification method for vortex sheet and tube structures in turbulent flows. Phys. Fluids 13 (12), 3756–3774.CrossRefGoogle Scholar
Horiuti, K. & Takagi, Y. 2005 Identification method for vortex sheet structures in turbulent flows. Phys. Fluids 17 (12), 121703.CrossRefGoogle Scholar
Jahanbakhshi, R., Vaghefi, N.S. & Madnia, C.K. 2015 Baroclinic vorticity generation near the turbulent/non-turbulent interface in a compressible shear layer. Phys. Fluids 27 (10), 105105.CrossRefGoogle Scholar
Jimenez, J. & Wray, A.A. 1998 On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285.CrossRefGoogle Scholar
Jiménez, J., Wray, A.A., Saffman, P.G. & Rogallo, R.S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Kang, S.-J., Tanahashi, M. & Miyauchi, T. 2007 Dynamics of fine scale eddy clusters in turbulent channel flows. J. Turbul. 8, N52.CrossRefGoogle Scholar
Kholmyansky, M., Tsinober, A. & Yorish, S. 2001 Velocity derivatives in the atmospheric surface layer at $Re_\lambda =10^{4}$. Phys. Fluids 13 (1), 311–314.CrossRefGoogle Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation. Intl J. Heat Fluid Flow 24 (6), 785–794.CrossRefGoogle Scholar
Kolář, V. 2007 Vortex identification: new requirements and limitations. Intl J. Heat Fluid Flow 28 (4), 638–652.CrossRefGoogle Scholar
Kozul, M., Chung, D. & Monty, J.P. 2016 Direct numerical simulation of the incompressible temporally developing turbulent boundary layer. J. Fluid Mech. 796, 437–472.CrossRefGoogle Scholar
LaRue, J.C. & Libby, P.A. 1974 Temperature fluctuations in the plane turbulent wake. Phys. Fluids 17 (11), 1956–1967.CrossRefGoogle Scholar
Maciel, Y., Robitaille, M. & Rahgozar, S. 2012 A method for characterizing cross-sections of vortices in turbulent flows. Intl J. Heat Fluid flow 37, 177–188.CrossRefGoogle Scholar
Matsubara, M., Alfredsson, P.H. & Segalini, A. 2020 Linear modes in a planar turbulent jet. J. Fluid Mech. 888, A26.CrossRefGoogle Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.CrossRefGoogle Scholar
Morinishi, Y., Lund, T.S., Vasilyev, O.V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143 (1), 90–124.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
Nagata, R., Watanabe, T., Nagata, K. & da Silva, C.B. 2020 Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence. Comput. Fluids 198, 104389.CrossRefGoogle Scholar
Namer, I. & Ötügen, M.V. 1988 Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers. Exp. Fluids 6 (6), 387–399.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 On the dynamical relevance of coherent vortical structures in turbulent boundary layers. J. Fluid Mech. 648, 325–349.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle 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
Ruetsch, G.R. & Maxey, M.R. 1991 Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids 3 (6), 1587–1597.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
Siggia, E.D. 1981 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406.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 in a jet. J. Fluid Mech. 685, 165–190.CrossRefGoogle Scholar
da Silva, C.B., Hunt, J.C.R., 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., 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 (5), 055101.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
Stanley, S.A., Sarkar, S. & Mellado, J.P. 2002 A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation. J. Fluid Mech. 450, 377–407.CrossRefGoogle Scholar
Takahashi, M., Iwano, K., Sakai, Y. & Ito, Y. 2019 Experimental investigation on destruction of Reynolds stress in a plane jet. Exp. Fluids 60 (3), 46.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 (4), 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
Terashima, O., Sakai, Y. & Ito, Y. 2018 Measurement of fluctuating temperature and POD analysis of eigenmodes in a heated planar jet. Exp. Therm. Fluid Sci. 92, 113–124.CrossRefGoogle Scholar
Terashima, O., Sakai, Y. & Nagata, K. 2012 Simultaneous measurement of velocity and pressure in a plane jet. Exp. Fluids 53 (4), 1149–1164.CrossRefGoogle Scholar
Thiesset, F., Schaeffer, V., Djenidi, L. & Antonia, R.A. 2014 On self-preservation and log-similarity in a slightly heated axisymmetric mixing layer. Phys. Fluids 26 (7), 075106.CrossRefGoogle Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence. Springer.CrossRefGoogle Scholar
Veynante, D. & Vervisch, L. 2002 Turbulent combustion modeling. Prog. Energy Combust. Sci. 28 (3), 193–266.CrossRefGoogle Scholar
Vincent, A. & Meneguzzi, M. 1994 The dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258, 245–254.CrossRefGoogle Scholar
Watanabe, T., Naito, T., Sakai, Y., Nagata, K. & Ito, Y. 2015 Mixing and chemical reaction at high Schmidt number near turbulent/nonturbulent interface in planar liquid jet. Phys. Fluids 27 (3), 035114.CrossRefGoogle Scholar
Watanabe, T., Riley, J.J., Nagata, K., Onishi, R. & Matsuda, K. 2018 a A localized turbulent mixing layer in a uniformly stratified environment. J. Fluid Mech. 849, 245–276.CrossRefGoogle Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 a Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26 (10), 105103.CrossRefGoogle Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 b Vortex stretching and compression near the turbulent/nonturbulent interface in a planar jet. J. Fluid Mech. 758, 754–785.CrossRefGoogle Scholar
Watanabe, T., Sakai, Y., Nagata, K. & Terashima, O. 2014 c Experimental study on the reaction rate of a second-order chemical reaction in a planar liquid jet. AIChE J. 60 (11), 3969–3988.CrossRefGoogle Scholar
Watanabe, T., da Silva, C.B., Nagata, K. & Sakai, Y. 2017 Geometrical aspects of turbulent/non-turbulent interfaces with and without mean shear. Phys. Fluids 29 (8), 085105.CrossRefGoogle Scholar
Watanabe, T., Tanaka, K. & Nagata, K. 2020 Characteristics of shearing motions in incompressible isotropic turbulence. Phys. Rev. Fluids 5 (7), 072601.CrossRefGoogle Scholar
Watanabe, T., Zhang, X. & Nagata, K. 2018 b Turbulent/non-turbulent interfaces detected in DNS of incompressible turbulent boundary layers. Phys. Fluids 30 (3), 035102.CrossRefGoogle Scholar
Watanabe, T., Zhang, X. & Nagata, K. 2019 Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation. Comput. Fluids 194, 104314.CrossRefGoogle Scholar
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
Wu, N., Sakai, Y., Nagata, K., Suzuki, H., Terashima, O. & Hayase, T. 2013 Analysis of flow characteristics of turbulent plane jets based on velocity and scalar fields using DNS. J. Fluid Sci. Technol. 8 (3), 247–261.CrossRefGoogle Scholar
Yamamoto, K. & Hosokawa, I. 1988 A decaying isotropic turbulence pursued by the spectral method. J. Phys. Soc. Japan 57 (5), 1532–1535.CrossRefGoogle Scholar
Zhou, Y. & Vassilicos, J.C. 2017 Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation. J. Fluid Mech. 821, 440–457.CrossRefGoogle Scholar