Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-29T11:24:48.031Z Has data issue: false hasContentIssue false

Purely helical absolute equilibria and chirality of (magneto)fluid turbulence

Published online by Cambridge University Press:  02 January 2014

Jian-Zhou Zhu
Affiliation:
WCI Center for Fusion Theory, National Fusion Research Institute, 169-148 Gwahak-ro, Daejeon, Korea Department of Modern Physics, University of Science and Technology of China, 230026 Hefei, PR China Life and Chinese Medicine Study Center, Gui-Lin Tang Lab., 46 Bayi Cun, 366025 Yong’an, Fujian, PR China
Weihong Yang
Affiliation:
Department of Modern Physics, University of Science and Technology of China, 230026 Hefei, PR China
Guang-Yu Zhu
Affiliation:
Life and Chinese Medicine Study Center, Gui-Lin Tang Lab., 46 Bayi Cun, 366025 Yong’an, Fujian, PR China

Abstract

Purely helical absolute equilibria of incompressible neutral fluids and plasmas (electron, single-fluid and two-fluid magnetohydrodynamics) are systematically studied with the help of helical (wave) representation and truncation, for genericities and specificities about helicity. A unique chirality selection and amplification mechanism and relevant insights, such as the one-chiral-sector-dominated states, among others, about (magneto)fluid turbulence follow.

Type
Papers
Copyright
©2013 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

Arnold, V. I. & Khesin, B. A. 1998 Topological Methods in Hydrodynamics. Springer.CrossRefGoogle Scholar
Barron, L. D. 1997 From cosmic chirality to protein structure and function: Lord Kelvin’s legacy. Q. J. Med. 90, 793800.Google Scholar
Berger, M. A. & Field, G. B. 1984 The topological properties of magnetic helicity. J. Fluid Mech. 147, 133148.CrossRefGoogle Scholar
Betchov, R. 1961 Semi-isotropic turbulence and helicoidal flows. Phys. Fluids 4, 925926.Google Scholar
Biferale, L., Musacchio, S. & Toschi, F. 2012 Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108, 104501104504.Google Scholar
Biskamp, D., Schwarz, E., Zeiler, A. & Celani & Drake, J. F. 1999 Electron magnetohydrodynamic turbulence. Phys. Plasmas 6, 751758.Google Scholar
Blackmond, D. G. 2010 The origin of bilogical homochirality. Cold Spring Harb. Perspect Biol. 2, a002147.Google Scholar
Brandenburg, A., Dobler, W. & Subramanian, K. 2002 Magnetic helicity in stellar dynamos: new numerical experiments. Astron. Nachr. 323, 99123.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1209.Google Scholar
Brissaud, A., Frisch, U., Leorat, J., Lesieur, M. & Mazure, M. 1973 Helicity cascades in isotropic turbulence. Phys. Fluids 16, 13661367.Google Scholar
Chen, Q. N., Chen, S. Y. & Eyink, G. L. 2003 The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15 (2), 361374.CrossRefGoogle Scholar
Chen, Q. N., Chen, S. Y., Eyink, G. L. & Holm, D. 2005 Resonant interactions in rotating homogeneous three-dimensional turbulence. J. Fluid Mech. 542, 139163.Google Scholar
Cho, J. 2011 Magnetic helicity conservation and inverse energy cascade in electron magnetohydrodynamic wave packets. Phys. Rev. Lett. 106, 191104191107.Google Scholar
Cintas, P. & Viedma, C. 2012 On the physical basis of asymmetry and homochirality. Chirality 24, 894908.CrossRefGoogle ScholarPubMed
Ditlevsen, P. D. & Giuliani, P. 2001 Dissipation in helical turbulence. Phys. Fluids 13, 35083509.Google Scholar
Eyink, G. L. 2008 Dissipative anomalies in singular Euler flows. Physica D 237, 19561968.Google Scholar
Eyink, G. L. & Sreenivasan, K. R. 2006 Onsager and the theory of turbulence. Rev. Mod. Phys. 78, 87135.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of Kolmogorov. Cambridge University Press.Google Scholar
Frisch, U., Kurien, S, Pandit, R., Pauls, W., Ray, S., Wirth, A. & Zhu, J.-Z. 2008 Hyperviscosity, Galerkin truncation and bottleneck of turbulence. Phys. Rev. Lett. 101, 114501114504.Google Scholar
Frisch, U., Pouquet, A., Leorat, J. & Mazure, A. 1975 Possibility of an inverse magnetic helicity cascade in magnetohydrodynamic turbulence. J. Fluid Mech. 68, 769778.CrossRefGoogle Scholar
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 20602072.Google Scholar
Galtier, S. 2006 Wave turbulence in incompressible hall magnetohydrodynamics. J. Plasma Phys. 72, 721769.CrossRefGoogle Scholar
Galtier, S. & Bhattacharjee, A. 2003 Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics. Phys. Plasmas 10, 30653076.Google Scholar
Hatfield, J. W. & Quake, S. R. 1999 Dynamic properties of an extended polymer in solution. Phys. Rev. Lett. 82, 35483551.Google Scholar
Ji, H. 1999 Turbulent dynamos and magnetic helicity. Phys. Rev. Lett. 83, 31983201.Google Scholar
Kelvin, Lord 1904 Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. C. J. Clay and Sons.Google Scholar
Kraichnan, R. H. 1958 Irreversible statistical mechanics of incompressible hydromagnetic turbulence. Phys. Rev. 109, 14071422.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.Google Scholar
Kraichnan, R. H. 1973 Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745752.Google Scholar
Kraichnan, R. H. & Montgomery, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547619.Google Scholar
Lee, T.-D. 1952 On some statistical properties of hydrodynamic and hydromagnetic fields. Q. Appl. Maths 10, 6974.Google Scholar
Lesieur, M. 1990 Turbulence in Fluids, 2nd edn. Kluwer.Google Scholar
Lessinnes, T., Plunian, F. & Carati, D. 2009 Helical shell models for MHD. Theor. Comput. Fluid Dyn. 23, 439450.Google Scholar
L’vov, V. S., Pomyalov, A. & Procaccia, I. 2002 Quasi-Gaussian statistics of hydrodynamic turbulence in $4/ 3+ \epsilon $ dimensions. Phys. Rev. Lett. 89, 064501064504.Google Scholar
Mandelbrot, B. B. 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331358.Google Scholar
Melander, V. & Hussain, F. 1993 Polarized vorticity dynamics in a vortex column. Phys. Fluids A 5, 19922003.CrossRefGoogle Scholar
Meneguzzi, M, Frisch, U & Pouquet, A 1981 Helical and nonhelical turbulent dynamos. Phys. Rev. Lett. 47, 10601063.Google Scholar
Meyrand, M. & Galtier, S. 2012 Spontaneous chiral symmetry breaking of hall magnetohydrodynmic turbulence. Phys. Rev. Lett. 109, 194501-15.Google Scholar
Miller, J. 1990 Statistical mechanics of Euler equations in two dimensions. Phys. Rev. Lett. 65, 21372140.Google Scholar
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117129.Google Scholar
Moffatt, H. K. 1970 Turbulent dynamo action at low magnetic Reynolds number. J. Fluid Mech. 41, 435452.CrossRefGoogle Scholar
Moffatt, H. K. 2008 Vortex dynamics: the legacy of Helmholtz and Kelvin. In Hamiltonian Dynamics, Vortex Structures, Turbulence (ed. Borisov, A. V., Kozlov, V. V., Mamaev, I. S. & Sokolovskiy, M. A.), pp. 113138. Springer.Google Scholar
Moses, H. E. 1971 Eigenfunctions of the curl operator, rotationally invariant Helmholtz theorem and applications to electromagnetic theory and fluid mechanics. SIAM J. Appl. Maths 21, 114130.Google Scholar
Perez, J. C., Mason, J., Boldyrev, S. & Cattaneo, F. 2012 On the energy spectrum of strong magnetohydrodynamic turbulence. Phys. Rev. X 2, 041005.Google Scholar
Petitjean, M. 2003 Chirality and symmetry measures: a transdisciplinary review. Entropy 5, 271312.Google Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321354.Google Scholar
Procaccia, I., L’vov, V. & Benzi, R. 2008 Colloquium: theory of drag reduction by polymers in wall bounded turbulence. Rev. Mod. Phys. 80, 225247.Google Scholar
Orszag, S. A. 1977 Statistical theory of turbulence. In Fluid Dynamics (ed. Balian, R. & Peube, J. L.), Les Houches 1973, pp. 237374. Gordon and Breach.Google Scholar
Robert, R. 2003 Statistical hydrodynamics (Onsager revisited). In Handbook of Mathematical Fluid Dynamics (ed. Friedlander, S. & Serre, D.), vol. 2, pp. 154. Gulf.Google Scholar
Ruban, V. P. 1999 Motion of magnetic flux lines in magnetohydrodynamics. Sov. Phys. JETP 89, 299310.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. & Tatsuno, T. 2009 Astrophysical gyrokinetics: Kinetic and fluid cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. 182, 310377.Google Scholar
Steinberg, V. 2009 Elastic stresses in random flow of a dilute polymer solution and the turbulent drag reduction problem. C. R. Phys. Paris 10, 728739.Google Scholar
Stenzel, R. L. 1999 Whistler waves in space and laboratory plasmas. J. Geophys. Res. 14, 1437914395.CrossRefGoogle Scholar
Stix, T. H. 1992 Waves in Plasmas. American Institute of Physics.Google Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4, 350363.Google Scholar
Woltjer, L. 1959 Hydromagnetic equilibrium II. Stability in the variational formulation. Proc. Natl Acad. Sci. USA 45, 769771.Google Scholar
Yamada, H., Katano, T., Kanai, K., Ishida, A. & Steinhauer, L. 2002 Equilibrium analysis of a flowing two-fluid plasma. Phys. Plasmas 11, 46054614.Google Scholar
Yang, Y.-T., Su, W.-D. & Wu, J.-Z. 2010 Helical-wave decomposition and applications to channel turbulence with streamwise rotation. J. Fluid Mech. 662, 91122.Google Scholar
Zhu, J.-Z. 2011 Fourier–Hankel/Bessel space absolute equilibria of 2D gyrokinetics. arXiv:1109.2511v1 [nlin.CD]: under revision for later journal publication.Google Scholar
Zhu, J.-Z. & Hammett, G. W. 2010 Gyrokinetic absolute equilibrium and turbulence. Phys. Plasmas 17, 122307-113.Google Scholar
Zhu, J.-Z. & Taylor, M. 2010 Intermittency and thermalization of turbulence. Chinese Phys. Lett. 27, 054702054705.Google Scholar