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Three-dimensional turbulence without vortex stretching

Published online by Cambridge University Press:  29 March 2021

Wouter J.T. Bos Open the ORCID record for Wouter J.T. Bos [Opens in a new window]
Wouter J.T. Bos*
Affiliation:
Univ Lyon, École Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR 5509, 36 Avenue Guy de Collongue, F-69134 Ecully, France
*
†Email address for correspondence: wouter.bos@ec-lyon.fr
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Abstract

We consider three-dimensional turbulence from which vortex stretching is removed. The resulting system conserves enstrophy, but does not conserve kinetic energy. Using spectral closure, it is shown that enstrophy is transferred to small scales by a direct cascade. The inviscid truncated system tends to an equipartition of enstrophy over wave vectors. No inverse cascade is observed once the scales larger than the forcing scale are in equipartition.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A121
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© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alexakis, A. 2017 Helically decomposed turbulence. J. Fluid Mech. 812, 752–770.CrossRefGoogle Scholar
Alexakis, A. & Brachet, M.-E. 2019 On the thermal equilibrium state of large-scale flows. J. Fluid Mech. 872, 594–625.CrossRefGoogle Scholar
Ashurst, W.T., Kerstein, A.R., Kerr, R.M. & Gibson, C.H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 2343–2353.CrossRefGoogle Scholar
Benavides, S.J. & Alexakis, A. 2017 Critical transitions in thin layer turbulence. J. Fluid Mech. 822, 364–385.CrossRefGoogle Scholar
Berera, A., Ho, R.D.J.G. & Clark, D. 2020 Homogeneous isotropic turbulence in four spatial dimensions. Phys. Fluids 32 (8), 085107.CrossRefGoogle Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1 (5), 497–504.CrossRefGoogle Scholar
Biferale, L., Musacchio, S. & Toschi, F. 2012 Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108 (16), 164501.CrossRefGoogle ScholarPubMed
Boldyrev, S.A. 1999 Turbulence without pressure in d dimensions. Phys. Rev. E 59 (3), 2971.CrossRefGoogle Scholar
Bos, W.J.T. & Bertoglio, J.P. 2006 Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids 18, 071701.CrossRefGoogle Scholar
Bos, W.J.T. & Bertoglio, J.P. 2013 Lagrangian Markovianized field approximation for turbulence. J. Turbul. 14, 99.CrossRefGoogle Scholar
Bos, W.J.T. & Rubinstein, R. 2013 On the strength of the nonlinearity in isotropic turbulence. J. Fluid Mech. 733, 158–170.CrossRefGoogle Scholar
Briard, A., Biferale, L. & Gomez, T. 2017 Closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence. Phys. Rev. Fluids 2 (10), 102602.CrossRefGoogle Scholar
Buaria, D., Bodenschatz, E. & Pumir, A. 2020 Vortex stretching and enstrophy production in high Reynolds number turbulence. arXiv:2006.01312.CrossRefGoogle Scholar
Burgers, J.M. 1950 Correlation problems in a one dimensional model of turbulence. Parts I–IV. Verh. K. Akad. Wet. Amsterdam 53, 247–260, 393–406; 718–731; 732–742.Google Scholar
Buzzicotti, M., Biferale, L. & Toschi, F. 2020 Statistical properties of turbulence in the presence of a smart small-scale control. Phys. Rev. Lett. 124 (8), 084504.CrossRefGoogle Scholar
Carbone, M. & Bragg, A.D. 2020 Is vortex stretching the main cause of the turbulent energy cascade? J. Fluid Mech. 883, R2.CrossRefGoogle Scholar
Celani, A., Musacchio, S. & Vincenzi, D. 2010 Turbulence in more than two and less than three dimensions. Phys. Rev. Lett. 104, 184506.CrossRefGoogle ScholarPubMed
Chen, H., Herring, J.R., Kerr, R.M. & Kraichnan, R.H. 1989 Non-Gaussian statistics in isotropic turbulence. Phys. Fluids A 1, 1844.CrossRefGoogle Scholar
Chertkov, M., Pumir, A. & Shraiman, B.I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11, 2394.CrossRefGoogle Scholar
Chevillard, L. & Meneveau, C. 2006 Lagrangian dynamics and statistical geometric structure of turbulence. Phys. Rev. Lett. 97, 174501.CrossRefGoogle ScholarPubMed
Cichowlas, C., Bonaïti, P., Debbasch, F. & Brachet, M. 2005 Effective dissipation and turbulence in spectrally truncated Euler flows. Phys. Rev. Lett. 95, 264502.CrossRefGoogle ScholarPubMed
Fang, L., Wu, T. & Bos, W.J.T. 2020 Staircase scaling of short-time energy transfer in turbulence. J. Turbul. 21 (4), 234–242.CrossRefGoogle Scholar
Favier, B., Guervilly, C. & Knobloch, E. 2019 Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 864, R1.CrossRefGoogle Scholar
Frisch, U., Lesieur, M. & Sulem, P.L. 1976 Crossover dimensions for fully developed turbulence. Phys. Rev. Lett. 37 (19), 1312.CrossRefGoogle Scholar
Frisch, U., Pomyalov, A., Procaccia, I. & Ray, S. 2012 Turbulence in noninteger dimensions by fractal Fourier decimation. Phys. Rev. Lett. 108 (7), 074501.CrossRefGoogle ScholarPubMed
Gotoh, T., Watanabe, Y., Shiga, Y., Nakano, T. & Suzuki, E. 2007 Statistical properties of four-dimensional turbulence. Phys. Rev. E 75 (1), 016310.CrossRefGoogle ScholarPubMed
Guala, M., Lüthi, B., Liberzon, A., Tsinober, A. & Kinzelbach, W. 2005 On the evolution of material lines and vorticity in homogeneous turbulence. J. Fluid Mech. 533, 339–359.CrossRefGoogle Scholar
Johnson, P.L. & Meneveau, C. 2016 Large-deviation statistics of vorticity stretching in isotropic turbulence. Phys. Rev. E 93 (3), 033118.CrossRefGoogle ScholarPubMed
Kraichnan, R.H. 1965 Lagrangian-history closure approximation for turbulence. Phys. Fluids 8, 575.CrossRefGoogle Scholar
Kraichnan, R.H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417.CrossRefGoogle Scholar
Kraichnan, R.H. 1973 Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745–752.CrossRefGoogle Scholar
Lanotte, A.S., Benzi, R., Malapaka, S.K., Toschi, F. & Biferale, L. 2015 Turbulence on a fractal Fourier set. Phys. Rev. Lett. 115 (26), 264502.CrossRefGoogle ScholarPubMed
Lee, T.D. 1952 On some statistical properties of hydrodynamical and magnetohydrodynamical fields. Q. Appl. Maths 10, 69.CrossRefGoogle Scholar
Leith, C.E. 1971 Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci. 28, 145–161.2.0.CO;2>CrossRefGoogle Scholar
Leprovost, N., Dubrulle, B. & Chavanis, P.-H. 2006 Dynamics and thermodynamics of axisymmetric flows: theory. Phys. Rev. E 73, 046308.CrossRefGoogle ScholarPubMed
Leslie, D.C. 1973 Developments in the Theory of Turbulence. Oxford University Press.Google Scholar
Naso, A., Monchaux, R., Chavanis, P.H. & Dubrulle, B. 2010 Statistical mechanics of Beltrami flows in axisymmetric geometry: theory reexamined. Phys. Rev. E 81, 066318.CrossRefGoogle ScholarPubMed
Orszag, S.A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.CrossRefGoogle Scholar
Plunian, F., Teimurazov, A., Stepanov, R. & Verma, M.K. 2020 Inverse cascade of energy in helical turbulence. J. Fluid Mech. 895, A13.CrossRefGoogle Scholar
Polyakov, A.M. 1995 Turbulence without pressure. Phys. Rev. E 52 (6), 6183.CrossRefGoogle Scholar
Qin, Z., Faller, H., Dubrulle, B., Naso, A. & Bos, W.J.T. 2020 Transition from non-swirling to swirling axisymmetric turbulence. Phys. Rev. Fluids 5 (6), 064602.CrossRefGoogle Scholar
Qu, B., Bos, W.J.T. & Naso, A. 2017 Direct numerical simulation of axisymmetric turbulence. Phys. Rev. Fluids 2, 094608.CrossRefGoogle Scholar
Qu, B., Naso, A. & Bos, W.J.T. 2018 Cascades of energy and helicity in axisymmetric turbulence. Phys. Rev. Fluids 3 (1), 014607.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Taylor, G.I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. Lond. A 164 (916), 15–23.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. The MIT Press.CrossRefGoogle Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence, vol. 483. Springer.CrossRefGoogle Scholar
Yamamoto, T., Shimizu, H., Inoshita, T., Nakano, T. & Gotoh, T. 2012 Local flow structure of turbulence in three, four, and five dimensions. Phys. Rev. E 86 (4), 046320.CrossRefGoogle ScholarPubMed