Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T14:15:22.706Z Has data issue: false hasContentIssue false
  • English
  • Français

The hydrodynamical alpha-effect in a compressible medium

Published online by Cambridge University Press:  26 April 2006

G. A. Khomenko ,
S. S. Moiseev  and
A. V. Tur
G. A. Khomenko
Affiliation:
Space Research Institute, Academy of Sciences, Moscow 117810, USSR
S. S. Moiseev
Affiliation:
Space Research Institute, Academy of Sciences, Moscow 117810, USSR
A. V. Tur
Affiliation:
Space Research Institute, Academy of Sciences, Moscow 117810, USSR
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of the interaction of large-scale vortices with small-scale homogeneous isotropic helical turbulence in a compressible medium is considered. Averaged equations are derived using a closure procedure which is based on the functional technique. It is shown that the averaged vorticity equation has solutions that grow exponentially in time and which describe the effect of amplification of large-scale helical vortices by turbulence (hydrodynamical α-effect). The dependence of the growth rate on the compressibility is analysed, the limiting cases of incompressible fluid and turbulence δ-correlated in time being considered. The applications of the hydrodynamical α-effect discussed include the Earth's atmosphere and interstellar gas of spiral galaxies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 225 , April 1991 , pp. 355 - 369
Copyright
© 1991 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

André, J. K. & Lesier, M. 1977 Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81, 187–207.Google Scholar
Batchelob, G. K.: 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Brissaud, A., Frisch, U., Leorat, J., Lesieur, M. & Mazure, A., 1973 Helicity cascade in fully developed isotropic turbulence. Phys. Fluids 16, 1366–1367.Google Scholar
Frisch, U., She, Z. S. & Sulem, P. L., 1987 Large-scale flow driven by anisotropic kinetic alpha effect. Physica 28D, 382–392.Google Scholar
Gvaramadze, V. V., Khomenko, G. A. & Tub, A. V., 1989 Large-scale vortices in helical turbulence of incompressible fluid. Geophys. Astrophys. Fluid Dyn. 46, 53–69 (preprint IKI, 1987, Pr-1210, Moscow (in Russian)).Google Scholar
Janke, E., Emde, F. & Lösch, F. 1960 Tafeln Höherer Funktionen. Stuttgart: Teubner.
Kraichnan, R. H.: 1973 Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745–752.Google Scholar
Krause, F. & Rädler, K.–H. 1980 Mean-Field Magnetohydrodynamics and Dynamo Theory. Berlin: Academic.
Krause, F. & Rüdigeb, G. 1974 On the Reynolds stresses in mean-field hydrodynamics. I. Incompressible homogeneous isotropic turbulence. Astron. Nachr. 295, 93–99.Google Scholar
Levich, E. & Tzvetkov, E., 1984 Helical cyclogenesis. Phys. Lett. 100A, 53–58.Google Scholar
Levich, E. & Tzvetkov, E., 1985 Helical inverse cascade in three-dimensional turbulence as a fundamental dominant mechanism in mesoscale atmospheric phenomena. Phys. Rep. 128, 1–37.Google Scholar
Moffatt, H. K.: 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
Moffatt, H. K.: 1981 Some developments in the theory of turbulence. J. Fluid Mech. 106, 27–47.Google Scholar
Moiseev, S. S., Rutkevich, P. B., Tur, A. V. & Yanovsky, V. V., 1987 Large-scale vortices of nontrivial topology in a turbulent convection. In Proc. Intl Conf. Plasma Phys., Vol. 2, pp. 75–79. Kiev: Nauk. Dunka.
Moiseev, S. S., Rutkevich, P. B., Tub, A. V. & Yanovsky, V. V., 1988 Vortex dynamos in a helical turbulent convection. Z. Exp. Teor. Fiz. 94, 144–153 (in Russian). (Engl. transl. Sov. Phys. JETP 67, 294–299.)Google Scholar
Moiseev, S. S., Sagdeev, R. Z., Tub, A. V., Khomenko, G. A. & Shukurov, A. M., 1983a Physical mechanism of amplification of vortex disturbances in the atmosphere. Dokl. Akad. Nauk SSSR, 273, 549–553 (in Russian). (Engl. transl. Sov. Phys. Dokl. 28, 925–928 (1983).)Google Scholar
Moiseev, S. S., Sagdeev, R. Z., Tub, A. V., Khomenko, G. A. & Yanovsky, V. V., 1983b A theory of large-scale structure origination in hydrodynamic turbulence. Z. Exp. Teor. Fiz. 85, 1979–1987 (in Russian). (Engl. transl. Sov. Phys. JETP 58, 1144 (1983).Google Scholar
Monin, A. S. & Yaglom, A. M., 1975 Statistical Fluid Mechanics. MIT Press.
Parker, E. N.: 1979 Cosmical Magnetic Fields. Clarendon.
Riehl, H.: 1976 Climate and Weather in the Tropics. Academic.
Ruzmaikin, A. A., Shukurov, A. M. & Sokoloff, D. D., 1988 Magnetic Fields of Galaxies, ch. 6. Dordrecht: Kluwer.
Sagdeev, R. Z., Moiseev, S. S., Rutkevich, P. B., Tub, A. V. & Yanovsky, V. V., 1987 On a possible mechanism of excitation of large-scale vortices in the atmosphere. In Proc. III Intl Symp. on Tropical Meteorology, Yalta, USSR, 1985 pp. 18–28. Gidrometeoizdat, Leningrad (in Russian).
Sagdeev, R. Z., Moiseev, S. S., Tur, A. V., Khomenko, G. A. & Yanovskii, V. V., 1984 Large-scale structures in hydrodynamical turbulence. In Self-Organization, Autowaves and Structures Far from Equilibrium (ed. V. I. Krinsky), pp. 74–76. Springer.
Steenbeck, M., Krause, F. & Rädler, K.-H. 1966 Berechnung der mittleren Lorentz-feldstärke V x B fur ein electrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte. beeinflubter bewegung. Z. Naturforsch. 21A, 369–376.Google Scholar
Sulem, P. L., She, Z. S., Scholl, H. & Frisch, U., 1989 Generation of large-scale structures in three-dimensional flow lacking parity-invariance. J. Fluid Mech. 205, 341–358.Google Scholar
Tur, A. V., Khomenko, G. A., Gvaramadze, V. V. & Chkhetiani, O. G., 1987 Helical structures in turbulent flows. In Proc. Intl Conf. Plasma Phys., vol. 2, pp. 203–206. Kiev: Nauk. Dumka.
Tur, A. V., Khomenko, G. A. & Yanovskii, V. V., 1984 Development of structures in stochastic systems and closure of the averaged equations. In Nonlinear and Turbulent Processes in Physics, vol. 2 (ed. R. Z. Sagdeev), pp. 1073–1078. Gordon & Breach.