Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T01:46:48.168Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse cascade of energy in helical turbulence

Published online by Cambridge University Press:  18 May 2020

Franck Plunian Open the ORCID record for Franck Plunian [Opens in a new window] ,
Andrei Teimurazov Open the ORCID record for Andrei Teimurazov [Opens in a new window] ,
Rodion Stepanov Open the ORCID record for Rodion Stepanov [Opens in a new window]  and
Mahendra Kumar Verma Open the ORCID record for Mahendra Kumar Verma [Opens in a new window]
Franck Plunian*
Affiliation:
Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre,38000Grenoble, France
Andrei Teimurazov
Affiliation:
Institute of Continuous Media Mechanics, Korolyov 1, Perm, 614013, Russia
Rodion Stepanov
Affiliation:
Institute of Continuous Media Mechanics, Korolyov 1, Perm, 614013, Russia
Mahendra Kumar Verma
Affiliation:
Department of Physics, Indian Institute of Technology, Kanpur208016, India
*
†Email address for correspondence: Franck.Plunian@univ-grenoble-alpes.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Using direct numerical simulation of hydrodynamic turbulence with helicity forcing applied at all scales, a near-maximum helical turbulent state is obtained, with an inverse energy cascade at scales larger than the energy forcing scale and a forward helicity cascade at scales smaller than the energy forcing scale. In contrast to previous studies using decimated triads, our simulations contain all possible triads. By computing the shell-to-shell energy fluxes, we show that the inverse energy cascade results from weakly non-local interactions among homochiral triads. Varying the helicity injection range of scales leads to necessary conditions to obtain an inverse energy cascade.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 895 , 25 July 2020 , A13
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

Alexakis, A. 2017 Helically decomposed turbulence. J. Fluid Mech. 812, 752–770.CrossRefGoogle Scholar
Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767–769, 1–101.Google Scholar
Biferale, L., Musacchio, S. & Toschi, F. 2012 Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108 (16), 164501.CrossRefGoogle ScholarPubMed
Biferale, L., Musacchio, S. & Toschi, F. 2013 Split energy-helicity cascades in three-dimensional homogeneous and isotropic turbulence. J. Fluid Mech. 730, 309–327.CrossRefGoogle Scholar
Brissaud, A., Frisch, U., Leorat, J., Lesieur, M. & Mazure, A. 1973 Helicity cascades in fully developed isotropic turbulence. Phys. Fluids 16, 1366–1367.CrossRefGoogle Scholar
Cambon, C. & Jacquin, J. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.CrossRefGoogle Scholar
Chen, Q., Chen, S. & Eyink, G. L. 2003a The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15 (2), 361–374.CrossRefGoogle Scholar
Chen, Q., Chen, S., Eyink, G. L. & Holm, D. D. 2003b Intermittency in the joint cascade of energy and helicity. Phys. Rev. Lett. 90 (21), 214503.CrossRefGoogle Scholar
Craya, A. 1958 Contribution à l’analyse de la turbulence associée à des vitesses moyennes. P.S.T. Ministère de l’Air (Paris) 345.Google Scholar
Gupta, A., Jayaraman, R., Chatterjee, A. G., Sadhukhan, S., Samtaney, R. & Verma, M. K. 2019 Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence. Phys. Rev. E 100, 053101.Google ScholarPubMed
Herbert, E., Daviaud, F., Dubrulle, B., Nazarenko, S. & Naso, A. 2012 Dual non-Kolmogorov cascades in a von Kármán flow. Europhys. Lett. 100 (4), 44003.CrossRefGoogle Scholar
Herring, J. R. 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859–872.CrossRefGoogle Scholar
Kessar, M., Plunian, F., Stepanov, R. & Balarac, G. 2015 Non-Kolmogorov cascade of helicity-driven turbulence. Phys. Rev. E 92, 031004.Google ScholarPubMed
Kraichnan, R. H. 1967 Inertial ranges in twodimensional turbulence. Phys. Fluids 10 (7), 1417–1423.CrossRefGoogle Scholar
Lessinnes, T., Plunian, F., Stepanov, R. & Carati, D. 2011 Dissipation scales of kinetic helicities in turbulence. Phys. Fluids 23 (3), 035108.CrossRefGoogle Scholar
Mininni, P. D., Alexakis, A. & Pouquet, A. 2006 Large-scale flow effects, energy transfer, and self-similarity on turbulence. Phys. Rev. E 74, 016303.Google ScholarPubMed
Mininni, P. D. & Pouquet, A. 2009 Helicity cascades in rotating turbulence. Phys. Rev. E 79, 026304.Google ScholarPubMed
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35 (1), 117–129.CrossRefGoogle Scholar
Moreau, J. J. 1961 Constantes d’un îlot tourbillonnaire en fluide parfait barotrope. C. R. Acad. Sci. Paris 252, 2810.Google Scholar
Musacchio, S. & Boffetta, G. 2019 Condensate in quasi-two-dimensional turbulence. Phys. Rev. Fluids 4, 022602.CrossRefGoogle Scholar
Okamoto, N., Yoshimatsu, K., Schneider, K., Farge, M. & Kaneda, Y. 2007 Coherent vortices in high resolution direct numerical simulation of homogeneous isotropic turbulence: A wavelet viewpoint. Phys. Fluids 19 (11), 115109.CrossRefGoogle Scholar
Plunian, F., Stepanov, R. & Verma, M. K. 2019 On uniqueness of transfer rates in magnetohydrodynamic turbulence. J. Plasma Phys. 85 (5), 905850507.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Qu, B., Naso, A. & Bos, W. J. T. 2018 Cascades of energy and helicity in axisymmetric turbulence. Phys. Rev. Fluids 3, 014607.CrossRefGoogle Scholar
Sadhukhan, S., Samuel, R., Plunian, F., Stepanov, R., Samtaney, R. & Verma, M. K. 2019 Enstrophy transfers in helical turbulence. Phys. Rev. Fluids 4, 084607.CrossRefGoogle Scholar
Sahoo, G., Alexakis, A. & Biferale, L. 2017 Discontinuous transition from direct to inverse cascade in three-dimensional turbulence. Phys. Rev. Lett. 118, 164501.CrossRefGoogle ScholarPubMed
Stepanov, R., Golbraikh, E., Frick, P. & Shestakov, A. 2015 Hindered energy cascade in highly helical isotropic turbulence. Phys. Rev. Lett. 115 (23), 234501.CrossRefGoogle ScholarPubMed
Stepanov, R., Teimurazov, A., Titov, V., Verma, M. K., Barman, S., Kumar, A. & Plunian, F. 2018 Direct numerical simulation of helical magnetohydrodynamic turbulence with Tarang code. In 2017 Ivannikov ISPRAS Open Conference (ISPRAS), pp. 90–96. IEEE.Google Scholar
Teimurazov, A. S., Stepanov, R. A., Verma, M. K., Barman, S., Kumar, A. & Sadhukhan, S. 2018 Direct numerical simulation of homogeneous isotropic helical turbulence with the TARANG code. J. Appl. Mech. Tech. Phys. 59 (7), 1279–1287.CrossRefGoogle Scholar
Verma, M. K. 2004 Statistical theory of magnetohydrodynamic turbulence: recent results. Phys. Rep. 401, 229–380.Google Scholar
Verma, M. K. 2019 Energy Transfers in Fluid Flows: Multiscale and Spectral Perspective. Cambridge University Press.CrossRefGoogle Scholar
Verma, M. K., Chatterjee, A. G., Yadav, R. K., Paul, S., Chandra, M. & Samtaney, R. 2013 Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations. Pramana-J. Phys. 81, 617–629.CrossRefGoogle Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids 4 (2), 350–363.CrossRefGoogle Scholar