Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T01:43:44.147Z Has data issue: false hasContentIssue false
  • English
  • Français

Dual channels of helicity cascade in turbulent flows

Published online by Cambridge University Press:  28 April 2020

Zheng Yan Open the ORCID record for Zheng Yan [Opens in a new window] ,
Xinliang Li ,
Changping Yu Open the ORCID record for Changping Yu [Opens in a new window] ,
Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window]  and
Shiyi Chen
Zheng Yan
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing100049, PR China
Xinliang Li
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing100049, PR China
Changping Yu*
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing100049, PR China
Jianchun Wang
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China
Shiyi Chen
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China State Key Laboratory of Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing100871, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulent flows. Through theoretical analyses, we find that there are two channels in the helicity cascade process, which differs dramatically from the traditional viewpoint. In this paper, we have conducted important research on the newly proposed dual-channel helicity cascade theory, including vortex dynamic processes, intermittent discrepancies, tensor geometries, etc. The first channel mainly originates from the vortex twisting process, and the second channel mainly originates from the vortex stretching process. Antisymmetric tensors are introduced to the derivations of dual-channel helicity cascade theory, and a complex rotation frame leads to a higher helicity transfer efficiency. By analysing data from direct numerical simulations of typical turbulent flows, we find that these two channels behave differently. The ensemble averages of helicity flux in different channels are equal in homogeneous and isotropic turbulence, while they are different in other types of turbulent flows. The intermittency of the second channel is stronger than that of the first channel. In addition, we find a novel mechanism of hindered or even inverse energy cascades, which could be attributed to the second-channel helicity flux.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 894 , 10 July 2020 , R2
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, 1–101.Google Scholar
Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.CrossRefGoogle ScholarPubMed
Andre, J. C. & Lesieur, M. 1977 Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81, 187–207.CrossRefGoogle Scholar
Ballouz, J. G. & Ouellette, N. T. 2018 Tensor geometry in the turbulent cascade. J. Fluid Mech. 835, 1048–1064.CrossRefGoogle Scholar
Biferale, L. 2003 Shell models of energy cascade in turbulence. Annu. Rev. Fluid Mech. 35, 441–468.CrossRefGoogle Scholar
Biferale, L., Musacchio, S. & Toschi, F. 2012 Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108, 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
Block, D., Teliban, I., Greiner, F. & Piel, A. 2006 Prospects and limitations of conditional averaging. Phys. Scr. T122, 25–33.Google Scholar
Brissaud, A. 1973 Helicity cascades in fully developed isotropic turbulence. Phys. Fluids 16, 1366–1367.CrossRefGoogle Scholar
Buzzicotti, M., Linkmann, M., Aluie, H., Biferale, L., Brasseur, J. & Meneveau, C. 2018 Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence. J. Turbul. 19, 167–197.CrossRefGoogle Scholar
Chen, Q., Chen, S. & Eyink, G. L. 2003a The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15, 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, 214503.CrossRefGoogle Scholar
Duquenne, A. M., Guiraud, P. & Bertrand, J. 1993 Swirl-induced improvement of turbulent mixing: laser study in a jet-stirred tubular reactor. Chem. Engng Sci. 48, 3805–3812.CrossRefGoogle Scholar
Eyink, G. L. 2006 Multi-scale gradient expansion of the turbulent stress tensor. J. Fluid Mech. 549, 159–190.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Graham, J., Kanov, K., Yang, X. I. A., Lee, M., Malaya, N., Lalescu, C. C., Burns, R., Eyink, G. L., Szalay, A., Moser, R. D. et al. 2016 A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J. Turbul. 17, 181–215.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
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283–325.CrossRefGoogle Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521–1536.2.0.CO;2>CrossRefGoogle Scholar
Lilly, D. K. 1986 The structure, energetic and propagation of rotating convective stroms. Part I. Energy exchange with the mean flow. J. Atmos. Sci. 43, 113–125.2.0.CO;2>CrossRefGoogle Scholar
Linkmann, M. 2018 Effects of helicity on dissipation in homogeneous box turbulence. J. Fluid Mech. 856, 79–102.CrossRefGoogle Scholar
Mininni, P. D. & Pouquet, A. 2009 Helicity cascades in rotating turbulence. Phys. Rev. E 79, 026304.Google ScholarPubMed
Mininni, P. D. & Pouquet, A. 2010 Rotating helical turbulence. II. Intermittency, scale invariance, and structures. Phys. Fluids 22, 035106.CrossRefGoogle Scholar
Moffatt, H. K. 1969 Degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117–129.CrossRefGoogle Scholar
Moffatt, H. K. 2014 Helicity and singular structures in fluid dynamics. Proc. Natl Acad. Sci. USA 111, 3663–3670.Google ScholarPubMed
Moffatt, H. K. 2017 Helicity-invariant even in a viscous fluid. Science 357, 448–449.Google Scholar
Moffatt, H. K. & Dormy, E. 2019 Self-Exciting Fluid Dynamos. Cambridge University Press.CrossRefGoogle Scholar
Moffatt, H. K. & Tsinober, A. 1992 Helicity in laminar and turbulence flow. Annu. Rev. Fluid Mech. 24, 281–312.CrossRefGoogle Scholar
Pelz, R. B., Yakhot, V., Orszag, S. A., Shtilman, L. & Levich, E. 1985 Velocity–vorticity patterns in turbulent flow. Phys. Rev. Lett. 54, 2505–2508.Google ScholarPubMed
Pouquet, A., Marino, R., Mininni, P. D. & Rosenberg, D. 2017 Dual constant-flux energy cascades to both large scales and small scales. Phys. Fluids 29, 111108.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
Salmon, R. 1998 Lectures on Geophysical Fluid Dynamics. Oxford University Press.Google Scholar
Scheeler, M. W., van Rees, W. M., Kedia, H., Kleckner, D. & Irvine, W. T. M. 2017 Complete measurement of helicity and its dynamics in vortex tubes. Science 357, 487–491.CrossRefGoogle ScholarPubMed
Shuster, M. D. 1993 A survey of attitude representations. J. Astronaut. Sci. 41, 439–517.Google Scholar
Stepanov, R., Golbraikh, E., Frick, P. & Shestakov, A. 2015 Hindered energy cascade in highly helical isotropic turbulence. Phys. Rev. Lett. 115, 234501.CrossRefGoogle ScholarPubMed
Słomka, J. & Dunkel, J. 2017 Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids. Proc. Natl Acad. Sci. USA 114, 2119–2124.CrossRefGoogle ScholarPubMed
Teimurazova, A. S., Stepanova, R. A., Vermab, M. K., Barmanb, S., Kumarb, A. & Sadhukhanb, S. 2018 Direct numerical simulation of homogeneous isotropic helical turbulence with the TARANG code. J. Appl. Mech. Tech. Phys. 59, 1279–1287.CrossRefGoogle Scholar
Teitelbaum, T. & Mininni, P. D. 2009 Effect of helicity and rotation on the free decay of turbulent flows. Phys. Rev. Lett. 103, 014501.CrossRefGoogle ScholarPubMed
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4, 350–363.CrossRefGoogle Scholar
Yu, C., Hong, R., Xiao, Z. & Chen, S. 2013 Subgrid-scale eddy viscosity model for helical turbulence. Phys. Fluids 25, 095101.Google Scholar