Hostname: page-component-669899f699-g7b4s Total loading time: 0 Render date: 2025-04-27T05:47:47.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Scale dependence of local shearing motion in decaying turbulence generated by multiple-jet interaction

Published online by Cambridge University Press:  08 October 2024

Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window] ,
Takahiro Mori ,
Kirari Ishizawa  and
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]
Tomoaki Watanabe*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan Education and Research Center for Flight Engineering, Nagoya University, Nagoya 464-8603, Japan
Takahiro Mori
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Kirari Ishizawa
Affiliation:
Undergraduate Department of Mechanical and Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Koji Nagata
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Scale dependence of local shearing motion is investigated experimentally in decaying homogeneous isotropic turbulence generated through multiple-jet interaction. The turbulent Reynolds number, based on the Taylor microscale, is between approximately 900 and 400. Velocity fields, measured using particle image velocimetry, are analysed through the triple decomposition of a low-pass filtered velocity gradient tensor, which quantifies the intensities of shear and rigid-body rotation at a given scale. These motions manifest predominantly as layer and tubular vortical structures, respectively. The scale dependence of the moments of velocity increments, associated with shear and rigid-body rotation, exhibits power-law behaviours. The scaling exponents for shear are in quantitative alignment with the anomalous scaling of the velocity structure functions, suggesting that velocity increments are influenced predominantly by shearing motion. In contrast, the exponents for rigid-body rotation are markedly smaller than those predicted by Kolmogorov scaling, reflecting the high intermittency of rigid-body rotation. The mean flow structure associated with shear at intermediate scales is investigated with conditional averages around locally intense shear regions in the filtered velocity field. The averaged flow field exhibits a shear layer structure with aspect ratio approximately 4.5, surrounded by rotating motion. The analysis at different scales reveals the existence of self-similar structures of shearing motion across various scales. The mean velocity jump across the shear layer increases with the layer thickness. This relationship is well predicted by Kolmogorov's second similarity hypothesis, which is useful in predicting the mean characteristics of shear layers across a wide range of scales.

JFM classification

Wakes/Jets: Jets Wakes/Jets: Shear layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 997 , 25 October 2024 , A14
Check for updates
Copyright
© The Author(s), 2024. 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.)

Article purchase

Temporarily unavailable

References

Akao, T., Watanabe, T. & Nagata, K. 2022 Vertical confinement effects on a fully developed turbulent shear layer. Phys. Fluids 34 (5), 055129.10.1063/5.0090686CrossRefGoogle Scholar
Arneodo, A., et al. 1996 Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett. 34 (6), 411.10.1209/epl/i1996-00472-2CrossRefGoogle Scholar
Bailey, S.C.C., et al. 2013 Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes. J. Fluid Mech. 715, 642–670.10.1017/jfm.2012.538CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48 (1), R29.10.1103/PhysRevE.48.R29CrossRefGoogle ScholarPubMed
Bermejo-Moreno, I., Pullin, D.I. & Horiuti, K. 2009 Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. J. Fluid Mech. 620, 121–166.10.1017/S002211200800476XCrossRefGoogle Scholar
Betchov, R. & Szewczyk, A. 1963 Stability of a shear layer between parallel streams. Phys. Fluids 6 (10), 1391–1396.CrossRefGoogle Scholar
Buaria, D. & Sreenivasan, K.R. 2023 Saturation and multifractality of Lagrangian and Eulerian scaling exponents in three-dimensional turbulence. Phys. Rev. Lett. 131 (20), 204001.10.1103/PhysRevLett.131.204001CrossRefGoogle Scholar
Carroll, P.L. & Blanquart, G. 2013 A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence. Phys. Fluids 25 (10), 105114.CrossRefGoogle Scholar
Castaing, B., Gagne, Y. & Hopfinger, E.J. 1990 Velocity probability density functions of high Reynolds number turbulence. Physica D 46 (2), 177–200.10.1016/0167-2789(90)90035-NCrossRefGoogle Scholar
Cattafesta, L.N. III & Sheplak, M. 2011 Actuators for active flow control. Annu. Rev. Fluid Mech. 43, 247–272.CrossRefGoogle Scholar
Clemens, N.T. & Mungal, M.G. 1991 A planar Mie scattering technique for visualizing supersonic mixing flows. Exp. Fluids 11 (2–3), 175–185.10.1007/BF00190296CrossRefGoogle Scholar
Coriton, B., Steinberg, A.M. & Frank, J.H. 2014 High-speed tomographic PIV and OH PLIF measurements in turbulent reactive flows. Exp. Fluids 55, 1–20.10.1007/s00348-014-1743-3CrossRefGoogle Scholar
Das, R. & Girimaji, S.S. 2020 Revisiting turbulence small-scale behavior using velocity gradient triple decomposition. New J. Phys. 22 (6), 063015.10.1088/1367-2630/ab8ab2CrossRefGoogle Scholar
Davidson, P.A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Dhruva, B., Tsuji, Y. & Sreenivasan, K.R. 1997 Transverse structure functions in high-Reynolds-number turbulence. Phys. Rev. E 56 (5), R4928.10.1103/PhysRevE.56.R4928CrossRefGoogle Scholar
Eisma, J., Westerweel, J., Ooms, G. & Elsinga, G.E. 2015 Interfaces and internal layers in a turbulent boundary layer. Phys. Fluids 27 (5), 055103.10.1063/1.4919909CrossRefGoogle Scholar
Elsinga, G.E., Ishihara, T., Goudar, M.V., da Silva, C.B. & Hunt, J.C.R. 2017 The scaling of straining motions in homogeneous isotropic turbulence. J. Fluid Mech. 829, 31–64.10.1017/jfm.2017.538CrossRefGoogle Scholar
Elsinga, G.E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.10.1017/S0022112010003381CrossRefGoogle Scholar
Elsinga, G.E. & Marusic, I. 2016 The anisotropic structure of turbulence and its energy spectrum. Phys. Fluids 28 (1), 011701.10.1063/1.4939471CrossRefGoogle Scholar
Enoki, R., Watanabe, T. & Nagata, K. 2023 Statistical properties of shear and nonshear velocity components in isotropic turbulence and turbulent jets. Phys. Rev. Fluids 8 (10), 104602.10.1103/PhysRevFluids.8.104602CrossRefGoogle Scholar
Fiscaletti, D., Buxton, O.R.H. & Attili, A. 2021 Internal layers in turbulent free-shear flows. Phys. Rev. Fluids 6 (3), 034612.10.1103/PhysRevFluids.6.034612CrossRefGoogle Scholar
Frisch, U., Sulem, P.-L. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87 (4), 719–736.10.1017/S0022112078001846CrossRefGoogle Scholar
Ganapathisubramani, B., Lakshminarasimhan, K. & Clemens, N.T. 2008 Investigation of three-dimensional structure of fine scales in a turbulent jet by using cinematographic stereoscopic particle image velocimetry. J. Fluid Mech. 598, 141–175.10.1017/S0022112007009706CrossRefGoogle Scholar
Gauding, M., Bode, M., Brahami, Y., Varea, É. & Danaila, L. 2021 Self-similarity of turbulent jet flows with internal and external intermittency. J. Fluid Mech. 919, A41.10.1017/jfm.2021.399CrossRefGoogle Scholar
Ghira, A.A., Elsinga, G.E. & da Silva, C.B. 2022 Characteristics of the intense vorticity structures in isotropic turbulence at high Reynolds numbers. Phys. Rev. Fluids 7 (10), 104605.CrossRefGoogle Scholar
Goto, S., Saito, Y. & Kawahara, G. 2017 Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers. Phys. Rev. Fluids 2 (6), 064603.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), 1065–1081.10.1063/1.1448296CrossRefGoogle Scholar
Goudar, M.V. & Elsinga, G.E. 2018 Tracer particle dispersion around elementary flow patterns. J. Fluid Mech. 843, 872–897.CrossRefGoogle Scholar
Hayashi, M., Watanabe, T. & Nagata, K. 2021 a Characteristics of small-scale shear layers in a temporally evolving turbulent planar jet. J. Fluid Mech. 920, A38.CrossRefGoogle Scholar
Hayashi, M., Watanabe, T. & Nagata, K. 2021 b The relation between shearing motions and the turbulent/non-turbulent interface in a turbulent planar jet. Phys. Fluids 33 (5), 055126.CrossRefGoogle Scholar
Hirota, M., Nishio, Y., Izawa, S. & Fukunishi, Y. 2017 Vortex stretching in a homogeneous isotropic turbulence. J. Phys.: Conf. Ser. 822 (1), 012041.Google Scholar
Isaza, J.C., Salazar, R. & Warhaft, Z. 2014 On grid-generated turbulence in the near- and far field regions. J. Fluid Mech. 753, 402–426.CrossRefGoogle Scholar
Iyer, K.P., Sreenivasan, K.R. & Yeung, P.K. 2020 Scaling exponents saturate in three-dimensional isotropic turbulence. Phys. Rev. Fluids 5 (5), 054605.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
Johnsen, E., et al. 2010 Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comput. Phys. 229 (4), 1213–1237.10.1016/j.jcp.2009.10.028CrossRefGoogle Scholar
Kailasnath, P., Sreenivasan, K.R. & Stolovitzky, G. 1992 Probability density of velocity increments in turbulent flows. Phys. Rev. Lett. 68 (18), 2766.10.1103/PhysRevLett.68.2766CrossRefGoogle ScholarPubMed
Kang, S.-J., Tanahashi, M. & Miyauchi, T. 2007 Dynamics of fine scale eddy clusters in turbulent channel flows. J. Turbul. 8, N52.10.1080/14685240701528544CrossRefGoogle Scholar
Keylock, C.J. 2018 The Schur decomposition of the velocity gradient tensor for turbulent flows. J. Fluid Mech. 848, 876–905.CrossRefGoogle Scholar
Kistler, A.L. & Vrebalovich, T. 1966 Grid turbulence at large Reynolds numbers. J. Fluid Mech. 26 (1), 37–47.CrossRefGoogle Scholar
Kitamura, T., Nagata, K., Sakai, Y., Sasoh, A., Terashima, O., Saito, H. & Harasaki, T. 2014 On invariants in grid turbulence at moderate Reynolds numbers. J. Fluid Mech. 738, 378–406.10.1017/jfm.2013.595CrossRefGoogle Scholar
Kolář, V. 2007 Vortex identification: new requirements and limitations. Intl J. Heat Fluid Flow 28 (4), 638–652.10.1016/j.ijheatfluidflow.2007.03.004CrossRefGoogle Scholar
Kolář, V. & Šístek, J. 2014 Recent progress in explicit shear-eliminating vortex identification. In Proceedings of the 19th Australasian Fluid Mechanics Conference. Australasian Fluid Mechanics Society Australia.Google Scholar
Kolmogorov, A.N. 1941 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
Kouchi, T., Fukuda, S., Miyai, S., Nagata, Y. & Yanase, S. 2019 Acetone-condensation nano-particle image velocimetry in a supersonic boundary layer. In AIAA Scitech 2019 Forum, p. 1821. American Institute of Aeronautics and Astronautics.10.2514/6.2019-1821CrossRefGoogle Scholar
Krogstad, P.-Å. & Davidson, P.A. 2012 Near-field investigation of turbulence produced by multi-scale grids. Phys. Fluids 24 (3), 035103.CrossRefGoogle Scholar
Kronborg, J. & Hoffman, J. 2023 The triple decomposition of the velocity gradient tensor as a standardized real Schur form. Phys. Fluids 35 (3), 031703.CrossRefGoogle Scholar
Leung, T., Swaminathan, N. & Davidson, P.A. 2012 Geometry and interaction of structures in homogeneous isotropic turbulence. J. Fluid Mech. 710, 453–481.CrossRefGoogle Scholar
Lin, S.J. & Corcos, G.M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.CrossRefGoogle Scholar
Liu, C., Gao, Y., Tian, S. & Dong, X. 2018 Rortex – a new vortex vector definition and vorticity tensor and vector decompositions. Phys. Fluids 30 (3), 035103.CrossRefGoogle Scholar
Lundgren, T.S. 1993 A small-scale turbulence model. Phys. Fluids 5 (6), 1472–1483.CrossRefGoogle Scholar
Marusic, I. & Monty, J.P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 49–74.10.1146/annurev-fluid-010518-040427CrossRefGoogle Scholar
Matsuda, K., Schneider, K. & Yoshimatsu, K. 2021 Scale-dependent statistics of inertial particle distribution in high Reynolds number turbulence. Phys. Rev. Fluids 6 (6), 064304.CrossRefGoogle Scholar
Matsushima, T., Nagata, K. & Watanabe, T. 2021 Wavelet analysis of shearless turbulent mixing layer. Phys. Fluids 33 (2), 025109.CrossRefGoogle Scholar
Melina, G., Bruce, P.J.K. & Vassilicos, J.C. 2016 Vortex shedding effects in grid-generated turbulence. Phys. Rev. Fluids 1 (4), 044402.CrossRefGoogle Scholar
Mohamed, M.S. & Larue, J.C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.10.1017/S0022112090002919CrossRefGoogle Scholar
Mori, T., Watanabe, T. & Nagata, K. 2024 Nearly homogeneous and isotropic turbulence generated by the interaction of supersonic jets. Exp. Fluids 65 (4), 47.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
Mouri, H., Hori, A. & Kawashima, Y. 2007 Laboratory experiments for intense vortical structures in turbulence velocity fields. Phys. Fluids 19 (5), 055101.10.1063/1.2720827CrossRefGoogle Scholar
Nagata, K., Saiki, T., Sakai, Y., Ito, Y. & Iwano, K. 2017 Effects of grid geometry on non-equilibrium dissipation in grid turbulence. Phys. Fluids 29 (1), 015102.CrossRefGoogle Scholar
Nagata, R., Watanabe, T., Nagata, K. & da Silva, C.B. 2020 b Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence. Comput. Fluids 198, 104389.CrossRefGoogle Scholar
Nagata, T., Noguchi, A., Kusama, K., Nonomura, T., Komuro, A., Ando, A. & Asai, K. 2020 a Experimental investigation on compressible flow over a circular cylinder at Reynolds number of between 1000 and 5000. J. Fluid Mech. 893, A13.CrossRefGoogle Scholar
Naso, A. & Pumir, A. 2005 Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence. Phys. Rev. E 72 (5), 056318.10.1103/PhysRevE.72.056318CrossRefGoogle ScholarPubMed
Neamtu-Halic, M.M., Mollicone, J.-P., Van Reeuwijk, M. & Holzner, M. 2021 Role of vortical structures for enstrophy and scalar transport in flows with and without stable stratification. J. Turbul. 22 (7), 393–412.CrossRefGoogle Scholar
Nieuwstadt, F.T., Westerweel, J. & Boersma, B. 2016 Introduction to Theory and Applications of Turbulent Flows. Springer.CrossRefGoogle Scholar
Pack, D.C. 1950 A note on Prandtl's formula for the wave-length of a supersonic gas jet. Q. J. Mech. Appl. Maths 3 (2), 173–181.CrossRefGoogle Scholar
Perry, A.E. & Chong, M.S. 1994 Topology of flow patterns in vortex motions and turbulence. Appl. Sci. Res. 53, 357–374.10.1007/BF00849110CrossRefGoogle 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
Pizzaia, A. & Rossmann, T. 2018 Effect of boundary layer thickness on transverse sonic jet mixing in a supersonic turbulent crossflow. Phys. Fluids 30 (11), 115104.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rabey, P.K., Wynn, A. & Buxton, O.R.H. 2015 The kinematics of the reduced velocity gradient tensor in a fully developed turbulent free shear flow. J. Fluid Mech. 767, 627–658.CrossRefGoogle Scholar
Saddoughi, S.G. & Veeravalli, S.V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.10.1017/S0022112094001370CrossRefGoogle Scholar
Sakurai, Y. & Ishihara, T. 2018 Relationships between small-scale fluid motions and inertial particle clustering in turbulence. J. Phys. Soc. Japan 87 (9), 093401.CrossRefGoogle Scholar
Saw, E.-W., Debue, P., Kuzzay, D., Daviaud, F. & Dubrulle, B. 2018 On the universality of anomalous scaling exponents of structure functions in turbulent flows. J. Fluid Mech. 837, 657–669.CrossRefGoogle Scholar
She, Z.-S. & Leveque, E. 1994 Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72 (3), 336.CrossRefGoogle ScholarPubMed
Shtilman, L., Spector, M. & Tsinober, A. 1993 On some kinematic versus dynamic properties of homogeneous turbulence. J. Fluid Mech. 247, 65–77.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
Sreenivasan, K.R. & Antonia, R.A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435–472.CrossRefGoogle Scholar
Takamure, K., Kato, H. & Uchiyama, T. 2023 Wake characteristics of sphere with circular uniaxial through-hole arranged perpendicularly to streamwise direction. Powder Technol. 415, 118175.CrossRefGoogle Scholar
Tan, S., Xu, X., Qi, Y. & Ni, R. 2023 Scalings and decay of homogeneous, nearly isotropic turbulence behind a jet array. Phys. Rev. Fluids 8 (2), 024603.CrossRefGoogle Scholar
Tang, S.L., Antonia, R.A., 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
Theunissen, R. 2010 Adaptive image interrogation for PIV: application to compressible flows and interfaces. PhD thesis, Delft University of Technology.Google Scholar
Thormann, A. & Meneveau, C. 2014 Decay of homogeneous, nearly isotropic turbulence behind active fractal grids. Phys. Fluids 26, 025112.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence. Springer.CrossRefGoogle Scholar
Vincent, A. & Meneguzzi, M. 1994 The dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258, 245–254.CrossRefGoogle Scholar
Wang, Y., Gao, Y. & Liu, C. 2018 Galilean invariance of Rortex. Phys. Fluids 30 (11), 111701.CrossRefGoogle Scholar
Watanabe, T. 2024 Efficient enhancement of turbulent entrainment by small-scale shear instability. J. Fluid Mech. 988, A20.CrossRefGoogle Scholar
Watanabe, T., Jaulino, R., Taveira, R.R., da Silva, C.B., Nagata, K. & Sakai, Y. 2017 Role of an isolated eddy near the turbulent/non-turbulent interface layer. Phys. Rev. Fluids 2 (9), 094607.CrossRefGoogle Scholar
Watanabe, T. & Nagata, K. 2018 Integral invariants and decay of temporally developing grid turbulence. Phys. Fluids 30 (10), 105111.CrossRefGoogle Scholar
Watanabe, T. & Nagata, K. 2022 Energetics and vortex structures near small-scale shear layers in turbulence. Phys. Fluids 34 (9), 095114.CrossRefGoogle Scholar
Watanabe, T. & Nagata, K. 2023 The response of small-scale shear layers to perturbations in turbulence. J. Fluid Mech. 963, A31.CrossRefGoogle Scholar
Watanabe, T., Riley, J.J., Nagata, K., Onishi, R. & Matsuda, K. 2018 A localized turbulent mixing layer in a uniformly stratified environment. J. Fluid Mech. 849, 245–276.CrossRefGoogle Scholar
Watanabe, T., Tanaka, K. & Nagata, K. 2020 Characteristics of shearing motions in incompressible isotropic turbulence. Phys. Rev. Fluids 5 (7), 072601(R).CrossRefGoogle Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39 (6), 1096–1100.10.1007/s00348-005-0016-6CrossRefGoogle Scholar
Zheng, Y., Nagata, K. & Watanabe, T. 2021 Turbulent characteristics and energy transfer in the far field of active-grid turbulence. Phy. Fluids 33 (11), 115119.CrossRefGoogle Scholar