Smart Structures and Systems

  • 제29권5호
  • /
  • Pages.747-755
  • /
  • 2022
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Hierarchical structure parameters in three dimensional turbulence: She-Leveque model

  • Ahmad, Imtiaz (Department of Mathematics, Mirpur University of Science and Technology (MUST)) ;
  • Hadj-Taieb, Lamjed (College of Engineering, Department of Mechanical Engineering, Prince Sattam Bin Abdulaziz University) ;
  • Hussain, Muzamal (Department of Mathematics, Government College Universit Faisalabad) ;
  • Khadimallah, Mohamed A. (Civil Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Alshoaibi, Adil (Department of Physics, College of Science, King Faisal University)
  • 투고 : 2020.09.16
  • 심사 : 2022.04.02
  • 발행 : 2022.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

Hierarchical structure parameters, proposed in She-Leveque model, are investigated for velocity components obtained from different flow types over a large range of Reynolds numbers 255 < Re𝜆 < 720. The values of intermittency parameter 𝛽, with respect to a fixed velocity component, are observed nearly same for all four types of turbulence. The parameter 𝛾, for streamwise velocity components is nearly the same but significantly different for vertical components in different flows. It is also observed that for both parameters, an obvious relation between the longitudinal and transverse components 𝛽T < 𝛽L (and 𝛾T < 𝛾L) always holds. However, the difference between 𝛽L and 𝛽T is found very small in all types of turbulent flows, we studied here. It is evidenced that at low Reynolds numbers, the deviations from K41 scaling are mainly due to the most intense structures and slightly because of more heterogeneous hierarchy of fluctuation structures. However, at higher Reynolds numbers the deviations seem as a consequence of the most intense structures only. Over all, the study suggests that the hierarchy parameter 𝛽 may be consider as a universal constant.

키워드

과제정보

This project was supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under research project no. 2019/01/10886

참고문헌

  1. AlSaleh, R.J. and Fuggini, C. (2020), "Combining GPS and accelerometers' records to capture torsional response of cylindrical tower", Smart Struct. Syst., 25(1), 111. http://doi.org/10.12989/sss.2020.25.1.111.
  2. Anselmet, F., Gagne, Y., Hopfinger, E. and Antonia, R. (1984), "High-order velocity structure functions in turbulent shear flows", J. Fluid Mech., 140, 63-89. https://doi.org/10.1017/S0022112084000513.
  3. Arani, A.G., Kolahchi, R. and Esmailpour, M. (2016), "Nonlinear vibration analysis of piezoelectric plates reinforced with carbon nanotubes using DQM", Smart Struct. Syst., 18, 787-800. http://doi.org/10.12989/sss.2016.18.4.787.
  4. Arefi, M. and Zenkour, A.M. (2017), "Nonlinear and linear thermo-elastic analyses of a functionally graded spherical shell using the Lagrange strain tensor", Smart Struct. Syst., 19, 33-38. DOI: https://doi.org/10.12989/sss.2017.19.1.033.
  5. Baroud, C.N., Plapp, B.B., Swinney, H.L. and She, Z.S. (2003), "Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows", Phys. Fluid., 15(8), 2091-2104. https://doi.org/10.1063/1.1577120.
  6. Bec, J., Biferale, L., Lanotte, A., Scagliarini, A. and Toschi, F. (2009), "Turbulent pair dispersion of inertial particles", J. Fluid Mech., 645, 497-528. https://doi.org/10.1017/S0022112009992783.
  7. Benzi, R., Biferale, L., Fisher, R., Lamb, D. and Toschi, F. (2010), "Inertial range Eulerian and Lagrangian statistics from numerical simulations of isotropic turbulence", J. Fluid Mech., 653, 221-244. https://doi.org/10.1017/S002211201000056X.
  8. Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. and Succi, S. (1993), "Extended self-similarity in turbulent flows", Phys. Rev. E, 48(1), R29. https://doi.org/10.1103/PhysRevE.48.R29.
  9. Benzi, R., Paladin, G., Parisi, G. and Vulpiani, A. (1984), "On the multifractal nature of fully developed turbulence and chaotic systems", J. Phys. A: Math. General, 17(18), 3521. https://doi.org/10.1088/0305-4470/17/18/021
  10. Berera, A. and Ho, R.D. (2018), "Chaotic properties of a turbulent isotropic fluid", Phys. Rev. Lett., 120(2), 024101. https://doi.org/10.1103/PhysRevLett.120.024101.
  11. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  12. Chavarria, G.R., Baudet, C. and Ciliberto, S. (1995), "Hierarchy of the energy dissipation moments in fully developed turbulence", Phys. Rev. Lett., 74(11), 1986. https://doi.org/10.1103/PhysRevLett.74.1986.
  13. Dubrulle, B. (1994), "Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance", Phys. Rev. Lett., 73(7), 959. https://doi.org/10.1103/PhysRevLett.73.959.
  14. Fisher, R.T., Kadanoff, L.P., Lamb, D.Q., Dubey, A., Plewa, T., Calder, A., ... & Needham, S.G (2008), "Terascale turbulence computation using the FLASH3 application framework on the IBM Blue Gene/L system", IBM J. Res. Develop., 52(1-2), 127-136. https://doi.org/10.1147/rd.521.0127.
  15. Friedrich, J. (2020), "Probability density functions in homogeneous and isotropic magneto-hydrodynamic turbulence", Atmosphere, 11(4), 382. https://doi.org/10.3390/atmos11040382.
  16. Frisch, U. and Kolmogorov, A.N. (1995), Turbulence: The Legacy of AN Kolmogorov, Cambridge University Press.
  17. Frisch, U., Sulem, P.L. and Nelkin, M. (1978), "A simple dynamical model of intermittent fully developed turbulence", J. Fluid Mech., 87(4), 719-736. https://doi.org/10.1017/S0022112078001846.
  18. Fukayama, D., Oyamada, T., Nakano, T., Gotoh, T. and Yamamoto, K. (2000), "Longitudinal structure functions in decaying and forced turbulence", J. Phys. Soc. JPN, 69(3), 701-715. https://doi.org/10.1143/JPSJ.69.701.
  19. Grossmann, S., Lohse, D. and Reeh, A. (1997), "Different intermittency for longitudinal and transversal turbulent fluctuations", Phys. Fluid., 9(12), 3817-3825. https://doi.org/10.1063/1.869516.
  20. Harris, V., Graham, J. and Corrsin, S. (1977), "Further experiments in nearly homogeneous turbulent shear flow", J. Fluid Mech., 81(4), 657-687. https://doi.org/10.1017/S0022112077002286.
  21. Iyer, K.P., Sreenivasan, K.R. and Yeung, P. (2017), "Reynolds number scaling of velocity increments in isotropic turbulence", Phys. Rev. E, 95(2), 021101. https://doi.org/10.1103/PhysRevE.95.021101.
  22. Iyer, K.P., Sreenivasan, K.R. and Yeung, P. (2020), "Scaling exponents saturate in three-dimensional isotropic turbulence", Phys. Rev. Fluid., 5(5), 054605. https://doi.org/10.1103/PhysRevFluids.5.054605.
  23. Jiang, X.Q., Gong, H., Liu, J.K., Zhou, M.D. and She, Z.S. (2006), "Hierarchical structures in a turbulent free shear flow", J. Fluid Mech., 569, 259. https://doi.org/10.1017/S0022112006002801.
  24. Kang, H.S., Chester, S. and Meneveau, C. (2003), "Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation", J. Fluid Mech., 480, 129-160. https://doi.org/10.1017/S0022112002003579.
  25. 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. https://doi.org/10.1017/S0022112062000518.
  26. Krommer, M., Vetyukova, Y. and Staudigl, E. (2016), "Nonlinear modelling and analysis of thin piezoelectric plates: buckling and post-buckling behavior", Smart Struct. Syst., 18(1), 155-181. https://doi.org/10.12989/sss.2016.18.1.155.
  27. Lee, S.Y., Huynh, T.C., Dang, N.L. and Kim, J.T. (2019), "Vibration characteristics of caisson breakwater for various waves, sea levels, and foundations", Smart Struct. Syst., 24(4), 525-539. https://doi.org/10.12989/sss.2019.24.4.525.
  28. Liu, J., She, Z.S., Guo, H., Li, L. and Ouyang, Q. (2004), "Hierarchical structure description of spatiotemporal chaos", Phys. Rev. E, 70(3), 036215. https://doi.org/10.1103/PhysRevE.70.036215.
  29. Liu, L. and She, Z.S. (2003), "Hierarchical structure description of intermittent structures of turbulence", Fluid Dyn. Res., 33(3), 261. https://doi.org/10.1016/S0169-5983(03)00071-6
  30. Liu, T. (2017), "An analytical solution for probability density function of stretching rate in homogeneous isotropic turbulence", Eur. J. Mech.-B/Fluid., 62, 42-50. https://doi.org/10.1016/j.euromechflu.2016.11.010.
  31. McComb, W.D. (2014), Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures, Vol. 162, OUP Oxford.
  32. Poff, N.L. and Zimmerman, J.K. (2010), "Ecological responses to altered flow regimes: A literature review to inform the science and management of environmental flows", Freshwater Biol., 55(1), 194-205. https://doi.org/10.1111/j.1365-2427.2009.02272.x.
  33. Poplawski, B., Mikulowski, G., Pisarski, D., Wiszowaty, R. and Jankowski, L. (2019), "Optimum actuator placement for damping of vibrations using the Prestress-Accumulation Release control approach", Smart Struct. Syst., 24(1), 27-35. DOI: 10.12989/sss.2019.24.1.027.
  34. Praskovsky, A.A., Gledzer, E.B., Karyakin, M.Y. and Zhou,Y. (1993), "The sweeping decorrelation hypothesis and energy-inertial scale interaction in high Reynolds number flows", J. Fluid Mech., 248, 493-511. https://doi.org/10.1017/S0022112093000862.
  35. Saw, E.W., Debue, P., Kuzzay, D., Daviaud, F. and Dubrulle, B. (2017), "On the universality of anomalous scaling exponents of structure functions in turbulent flows", J. Fluid Mech., 837, 657-669. https://doi.org/10.1017/jfm.2017.848.
  36. She, Z.S. and Leveque, E. (1994), "Universal scaling laws in fully developed turbulence", Phys. Rev. Lett., 72(3), 336. https://doi.org/10.1103/PhysRevLett.72.336.
  37. She, Z.S. and Zhang, Z.X. (2009), "Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems", Acta Mechanica Sinica, 25(3), 279-294. https://doi.org/10.1007/s10409-009-0257-3.
  38. She, Z.S., Ren, K., Lewis, G.S. and Swinney, H.L. (2001), "Scalings and structures in turbulent Couette-Taylor flow", Phys. Rev. E, 64(1), 016308. https://doi.org/10.1103/PhysRevE.64.016308.
  39. Shen, X. and Warhaft, Z. (2002), "Longitudinal and transverse structure functions in sheared and unsheared wind-tunnel turbulence", Phys. Fluid., 14(1), 370-381. https://doi.org/10.1063/1.1421059.
  40. Shih, L.H., Koseff, J.R., Ivey, G.N. and Ferziger, J.H. (2005), "Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations", J. Fluid Mech., 525, 193. https://doi.org/10.1017/S0022112004002587.
  41. Tohidi, H., Hosseini-Hashemi, S.H. and Maghsoudpour, A. (2018), "Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory", Smart Struct. Syst., 22(5), 527-546. https://doi.org/10.12989/sss.2018.22.5.527.
  42. Tong, C. (2001), "Measurements of conserved scalar filtered density function in a turbulent jet", Phys. Fluid., 13(10), 2923-2937. https://doi.org/10.1063/1.1402171.
  43. Wang, L. (2010), "On properties of fluid turbulence along streamlines", J. Fluid Mech., 648, 183. https://doi.org/10.1017/S0022112009993041.
  44. Yeh, J.Y. (2016), "Vibration characteristic analysis of sandwich cylindrical shells with MR elastomer", Smart Struct. Syst., 18(2), 233-247. https://doi.org/10.12989/sss.2016.18.2.233.
  45. Zahrai, S.M. and Kakouei, S. (2019), "Shaking table tests on a SDOF structure with cylindrical and rectangular TLDs having rotatable baffles", Smart Struct. Syst., 24(3), 391-401. https://doi.org/10.12989/sss.2019.24.3.391.