Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-22T19:59:23.276Z Has data issue: false hasContentIssue false
  • English
  • Français

Slow spectral transfer and energy cascades in isotropic turbulence

Published online by Cambridge University Press:  07 December 2020

Sualeh Khurshid ,
Diego A. Donzis Open the ORCID record for Diego A. Donzis [Opens in a new window]  and
Katepalli R. Sreenivasan
Sualeh Khurshid
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX, USA
Diego A. Donzis*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX, USA
Katepalli R. Sreenivasan
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX, USA Department of Mechanical and Aerospace Engineering, Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
*
†Email address for correspondence: donzis@tamu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A database of highly resolved direct numerical simulations of three-dimensional isotropic turbulence, with Taylor microscale Reynolds numbers ranging from ${\approx }3$ to 400, and grid sizes up to $2048^3$, is used to analyse the temporal behaviours of spectral transfer and energy that result from low-wavenumber forcing. The temporal behaviours of the energy and energy transfer spectra are analysed using single-time and time-delay statistics. Results show that the energy transfer across a given wavenumber in the inertial range fluctuates by an order of magnitude around its temporal average, and only slow fluctuations have the property of being unidirectional, consistent with classical cascade concepts. All small scales, roughly beyond $k\eta > 0.3$, respond essentially instantly to changes at the large scale.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A21
Check for updates
Copyright
© The Author(s), 2020. 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

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bos, W. J. T. & Rubinstein, R. 2017 Dissipation in unsteady turbulence. Phys. Rev. Fluids 2, 022601.CrossRefGoogle Scholar
Bos, W. J. T., Shao, L. & Bertoglio, J. P. 2007 Spectral imbalance and the normalized dissipation rate of turbulence. Phys. Fluids 19, 045101.CrossRefGoogle Scholar
Brasseur, J. G. 1991 Comments on the Kolmogorov hypotheses of isotropy in the small scales. AIAA Paper (91-0230).CrossRefGoogle Scholar
Brasseur, J. G. & Wei, C. H. 1994 Interscale dynamics and local isotropy in high Reynolds number turbulence within triadic interactions. Phys. Fluids 6, 842.CrossRefGoogle Scholar
Cardesa, J. I., Vela-Martín, A., Dong, S. & Jiménez, J. 2015 The temporal evolution of the energy flux across scales in homogeneous turbulence. Phys. Fluids 27, 111702.CrossRefGoogle Scholar
Domaradzki, J. A. 1988 Analysis of energy-transfer in direct numerical simulations of isotropic turbulence. Phys. Fluids 31, 2747–2749.CrossRefGoogle Scholar
Domaradzki, J. A. & Carati, D. 2007 An analysis of the energy transfer and the locality of nonlinear interactions in turbulence. Phys. Fluids 19, 085112.CrossRefGoogle Scholar
Domaradzki, J. A. & Rogallo, R. S. 1990 Local energy-transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids 2, 413–426.CrossRefGoogle Scholar
Domaradzki, J. A., Teaca, B. & Carati, D. 2009 Locality properties of the energy flux in turbulence. Phys. Fluids 21, 025106.CrossRefGoogle 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
Donzis, D. A. & Yeung, P. K. 2010 Resolution effects and scaling in numerical simulations of passive scalar mixing in turbulence. Physica D 239, 1278–1287.CrossRefGoogle Scholar
Eswaran, V. & Pope, S. B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16, 257–278.CrossRefGoogle Scholar
Falkovich, G. 1994 Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411–1414.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
George, W. K. & Wang, H. 2004 The spectral transfer in isotropic turbulence. In IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow (ed. T. B. Gatskii, S. Sarkar & G. Speziale), pp. 223–228. Springer.CrossRefGoogle Scholar
Horiuti, K. & Tamaki, T. 2013 Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation. Phys. Fluids 25, 125104.CrossRefGoogle Scholar
Ishihara, T., Morishita, K., Yokokawa, M., Uno, A. & Kaneda, Y. 2016 Energy spectrum in high-resolution direct numerical simulations of turbulence. Phys. Rev. Fluids 1, 082403.CrossRefGoogle Scholar
Kholmyansky, M. & Tsinober, A. 2008 Kolmogorov 4/5 law, nonlocality, and sweeping decorrelation hypothesis. Phys. Fluids 20, 041704.CrossRefGoogle Scholar
Khurshid, S., Donzis, D. A. & Sreenivasan, K. R. 2018 Energy spectrum in the dissipation range. Phys. Rev. Fluids 3, 082601.CrossRefGoogle Scholar
Kraichnan, R. H. 1977 Eulerian and Lagrangian renormalization in turbulence theory. J. Fluid Mech. 83, 349–374.CrossRefGoogle Scholar
Küchler, C., Bewley, G. & Bodenschatz, E. 2019 Experimental study of the bottleneck in fully developed turbulence. J. Stat. Phys. 175, 617–639.CrossRefGoogle Scholar
Lumley, J. L. 1992 Some comments on turbulence. Phys. Fluids A 4, 203–211.CrossRefGoogle Scholar
McComb, W. D. 2014 Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures. Oxford University Press.CrossRefGoogle Scholar
Meneveau, C. & Lund, T. S. 1994 On the lagrangian nature of the turbulence energy cascade. Phys. Fluids 6, 2820–2825.CrossRefGoogle Scholar
Mininni, P. D., Alexakis, A. & Pouquet, A. 2008 Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws. Phys. Rev. E 77, 036306.CrossRefGoogle ScholarPubMed
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.Google Scholar
Nelkin, M. & Tabor, M. 1990 Time correlations and random sweeping in isotropic turbulence. Phys. Fluids A 2, 81–83.CrossRefGoogle Scholar
Ohkitani, K. & Kida, S. 1992 Triad interactions in a forced turbulence. Phys. Fluids 4, 794–802.CrossRefGoogle Scholar
Praskovsky, A. A., Gledzer, E. B., Karyakin, M. Y. & Zhou, Y. 1993 The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows. J. Fluid Mech. 248, 493–511.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2018 Homogeneous Turbulence Dynamics. Springer.CrossRefGoogle Scholar
Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Van Atta, C. W. & Wyngaard, J. C. 1975 On higher-order spectra of turbulence. J. Fluid Mech. 72, 673–694.CrossRefGoogle Scholar
Verma, M. K. & Donzis, D. A. 2007 Energy transfer and bottleneck effect in turbulence. J. Phys. A 40, 4401–4412.CrossRefGoogle Scholar
Yeung, P. K. & Brasseur, J. G. 1991 The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales. Phys. Fluids 3, 884–897.CrossRefGoogle Scholar
Yeung, P. K., Sreenivasan, K. R. & Pope, S. B. 2018 Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence. Phys. Rev. Fluids 3, 064603.CrossRefGoogle Scholar
Yoshizawa, A. 1994 Nonequilibrium effect of the turbulent-energy-production process on the inertial-range energy spectrum. Phys. Rev. E 49, 4065.CrossRefGoogle ScholarPubMed