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Helically decomposed turbulence

Published online by Cambridge University Press:  06 January 2017

Alexandros Alexakis
Alexandros Alexakis*
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure, PSL Research University; Université Paris Diderot Sorbonne Paris-Cité; Sorbonne Universités UPMC Univ Paris 06; CNRS; 24 rue Lhomond, 75005 Paris, France
*
†Email address for correspondence: alexakis@lps.ens.fr
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Abstract

A decomposition of the energy and helicity fluxes is used to analyse turbulent hydrodynamic flows. The decomposition is based on the projection of the flow to a helical basis. This allows the roles of interactions among modes of different helicities to be investigated separately. The proposed formalism is applied to large-scale numerical simulations of non-helical and helical flows, where the decomposed fluxes are explicitly calculated. It is shown that the total energy flux can be split into three fluxes that independently remain constant in the inertial range. One of these fluxes which corresponds to the interactions of fields with the same helicity is negative, implying the presence of an inverse cascade that is ‘hidden’ inside the forward cascade. Similarly to the energy flux, it is also shown that the helicity flux can be decomposed into two fluxes that remain constant in the inertial range. Implications of these results as well as possible new directions for investigations are discussed.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 752 - 770
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Copyright
© 2017 Cambridge University Press 

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References

Alexakis, A., Mininni, P. D. & Pouquet, A. 2005 Imprint of large-scale flows on turbulence. Phys. Rev. Lett. 95 (26), 264503.Google Scholar
Baerenzung, J., Mininni, P. D., Pouquet, A. & Rosenberg, D. 2011 Spectral modeling of turbulent flows and the role of helicity in the presence of rotation. J. Atmos. Sci. 68, 2757–2770.CrossRefGoogle Scholar
Baerenzung, J., Politano, H., Ponty, Y. & Pouquet, A. 2008 Spectral modeling of turbulent flows and the role of helicity. Phys. Rev. E 77 (4), 046303.Google ScholarPubMed
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.Google Scholar
Borue, V. & Orszag, S. A. 1997 Spectra in helical three-dimensional homogeneous isotropic turbulence. Phys. Rev. E 55 (6), 7005.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209.Google Scholar
Brissaud, A., Frisch, U., Leorat, J., Lesieur, M. & Mazure, A. 1973 Helicity cascades in fully developed isotropic turbulence. Phys. Fluids 16 (8), 1366–1367.CrossRefGoogle Scholar
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.Google 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, Q., Chen, S. & Eyink, G. L. 2003 The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15 (2), 361–374.Google Scholar
Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S. & Wynne, S. 1998 Camassa–Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Lett. 81 (24), 5338.Google Scholar
Chen, S., Holm, D. D., Margolin, L. G. & Zhang, R. 1999 Direct numerical simulations of the Navier–Stokes alpha model. Physica D 133 (1), 66–83.Google Scholar
Constantin, P. & Majda, A. 1988 The Beltrami spectrum for incompressible fluid flows. Commun. Math. Phys. 115, 435–456.Google Scholar
Craya, A.1958 Contribution a l’analyse de la turbulence associée a des vitesses moyennes. Sci. Tech. du Ministere de l’Air (France) 345.Google Scholar
Dallas, V., Fauve, S. & Alexakis, A. 2015 Statistical equilibria of large scales in dissipative hydrodynamic turbulence. Phys. Rev. Lett. 115 (20), 204501.Google Scholar
De Pietro, M., Biferale, L. & Mailybaev, A. A. 2015 Inverse energy cascade in nonlocal helical shell models of turbulence. Phys. Rev. E 92 (4), 043021.Google ScholarPubMed
De Pietro, M., Mailybaev, A. A. & Biferale, L.2016 Chaotic and regular instantons in helical shell models of turbulence. Preprint, arXiv:1608.00742.Google Scholar
Deusebio, E., Boffetta, G., Lindborg, E. & Musacchio, S. 2014 Dimensional transition in rotating turbulence. Phys. Rev. E 90, 023005.Google Scholar
Ditlevsen, P. D. & Giuliani, P. 2001a Cascades in helical turbulence. Phys. Rev. E 63 (3), 036304.Google ScholarPubMed
Ditlevsen, P. D. & Giuliani, P. 2001b Dissipation in helical turbulence. Phys. Fluids 13 (11), 3508–3509.Google Scholar
Falkovich, G. 1994 Bottleneck phenomenon in developed turbulence. Phys. Fluids 6 (4), 1411.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.Google Scholar
Gilbert, A. 2002 Magnetic helicity in fast dynamos. Geophys. Astrophys. Fluid Dyn. 96 (2), 135–151.Google Scholar
Gilbert, A. D. & Childress, S. 1995 Stretch, Twist, Fold, the Fast Dynamo, Lecture Notes in Physics Monographs, vol. 37. Springer.Google Scholar
Herring, J. R. 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17 (5), 859–872.Google Scholar
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437.Google Scholar
de Karman, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164, 192–215.Google Scholar
Kessar, M., Plunian, F., Stepanov, R. & Balarac, G. 2015 Non-Kolmogorov cascade of helicity-driven turbulence. Phys. Rev. E 92 (3), 031004.Google Scholar
Kraichnan, R. H. 1973 Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745–752.Google Scholar
Kurien, S., Taylor, M. A. & Matsumoto, T. 2004 Cascade time scales for energy and helicity in homogeneous isotropic turbulence. Phys. Rev. E 69 (6), 066313.Google Scholar
Leith, C. E. 1990 Stochastic backscatter in a subgrid-scale model: plane shear mixing layer. Phys. Fluids 2 (3), 297–299.CrossRefGoogle Scholar
Lesieur, M.1972 Décomposition d’un champ de vitesse non divergent en ondes d’hélicité. Tech. Rep. Observatoire de Nice.Google Scholar
Lessinnes, T., Plunian, F., Stepanov, R. & Carati, D. 2011 Dissipation scales of kinetic helicities in turbulence. Phys. Fluids 23 (3), 035108.Google Scholar
Linkmann, M., Berera, A., McKay, M. & Jäger, J. 2016a Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence. J. Fluid Mech. 791, 61–96.Google Scholar
Linkmann, M., Sahoo, G., McKay, M., Berera, A. & Biferale, L.2016b Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition. Preprint, arXiv:1609.01781.Google Scholar
Lohse, D. & Müller-Groeling, A. 1995 Bottleneck effects in turbulence: scaling phenomena in r versus p space. Phys. Rev. Lett. 74 (10), 1747.Google Scholar
Martinez, D. O., Chen, S., Doolen, G. D., Kraichnan, R. H., Wang, L.-P. & Zhou, Y. 1997 Energy spectrum in the dissipation range of fluid turbulence. J. Plasma Phys. 57 (01), 195–201.CrossRefGoogle Scholar
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Menon, S., Yeung, P.-K. & Kim, W.-W. 1996 Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence. Comput. Fluids 25 (2), 165–180.Google 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 Scholar
Mininni, P. D., Rosenberg, D., Reddy, R. & Pouquet, A. 2011 A hybrid mpi–openmp scheme for scalable parallel pseudospectral computations for fluid turbulence. Parallel Comput. 37 (6), 316–326.CrossRefGoogle Scholar
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35 (1), 117–129.Google Scholar
Moffatt, H. K. 2014 Note on the triad interactions of homogeneous turbulence. J. Fluid Mech. 741, R3.Google Scholar
Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3 (7), 1766–1771.Google Scholar
Rathmann, N. M. & Ditlevsen, P. D.2016a Pseudo-invariants causing inverse energy cascades in three-dimensional turbulence. Preprint arXiv:1610.03879.Google Scholar
Rathmann, N. M. & Ditlevsen, P. D. 2016b The role of helicity in triad interactions in 3D turbulence investigated by a new shell model. Phys. Rev. E 94, 033115.Google Scholar
Sahoo, G. & Biferale, L. 2015 Disentangling the triadic interactions in Navier–Stokes equations. Eur. Phys. J. E 38 (10), 1–8.Google Scholar
Sahoo, G., Bonaccorso, F. & Biferale, L. 2015 Role of helicity for large- and small-scale turbulent fluctuations. Phys. Rev. E 92 (5), 051002.Google Scholar
Sahoo, G., De Pietro, M. & Biferale, L.2016 Helicity statistics in homogeneous and isotropic turbulence and turbulence models. Preprint arXiv:1607.05518.Google Scholar
Schumann, U. 1995 Stochastic backscatter of turbulence energy and scalar variance by random subgrid-scale fluxes. Proc. R. Soc. Lond. A 451, 293–318.Google Scholar
Seshasayanan, K. & Alexakis, A. 2016 Critical behavior in the inverse to forward energy transition in two-dimensional magnetohydrodynamic flow. Phys. Rev. E 93, 013104.Google ScholarPubMed
Seshasayanan, K., Benavides, S. J. & Alexakis, A. 2014 On the edge of an inverse cascade. Phys. Rev. E 90, 051003.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I: the basic experiment*. Mon. Weath. Rev. 91 (3), 99–164.Google Scholar
Sozza, A., Boffetta, G., Muratore-Ginanneschi, P. & Musacchio, S. 2015 Dimensional transition of energy cascades in stably stratified forced thin fluid layers. Phys. Fluids 27 (3), 035112.Google Scholar
Stepanov, R., Frick, P. & Mizeva, I. 2014 Joint inverse cascade of magnetic energy and magnetic helicity in MHD turbulence. Astrophys. J. Lett. 798 (2), L35.CrossRefGoogle Scholar
Stepanov, R., Golbraikh, E., Frick, P. & Shestakov, A. 2015 Hindered energy cascade in highly helical isotropic turbulence. Phys. Rev. Lett. 115 (23), 234501.Google Scholar
Vainshtein, S. I. & Zel’dovich, Y. B. 1972 On the origin of magnetic fields in astrophysics. (turbulence mechanisms ‘dynamo’). Usp. Fiz. Nauk 106, 431–457.Google Scholar
Verma, M. K., Ayyer, A., Debliquy, O., Kumar, S. & Chandra, A. V. 2005 Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence. Pramana 65 (2), 297–310.Google Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4, 350–363.Google Scholar