NONLINEAR DYNAMO IN A ROTATING ELECTRICALLY CONDUCTING FLUID

  • M. I. Kopp Institute for Single Cristals, Nat. Academy of Science Ukraine,Lenine Ave.60, Kharkov 31001,Ukraine https://orcid.org/0000-0001-7457-3272
  • A. V. Tur Universite Toulouse [UPS], CNRS, Institute of Research for Astrophysics and Planetology 9 avenue du Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
  • V. V. Yanovsky Institute for Single Cristals, Nat. Academy of Science Ukraine, Lenine Ave.60, Kharkov 31001,Ukraine V.N. Karazin Kharkiv National UniversitySq. Svobody 4, Kharkiv, 61022 Ukraine https://orcid.org/0000-0003-0461-749X
Keywords: equations of magnetohydrodynamics, Coriolis force, multiscale asymptotic expansions, small-scale turbulence, α- effect, spiral kinks

Abstract

We found a new large-scale instability, which arises in the rotating conductive fluid with small-scale turbulence. Turbulence is generated by small-scale external force with a low Reynolds number. The theory is built simply by the method of multiscale asymptotic expansions. Nonlinear equations for vortex and magnetic perturbations obtained in the third order for small Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The large-scale increments of the instability, correspond to generation as the vortex and magnetic disturbances. This type of instability is classified as hydrodynamic and MHD alpha-effect. We studied the stationary regimes of nonlinear equations of magneto-vortex dynamo. In the limit of weakly conducting fluid found stationary solutions in the form of helical kinks. In the limit of high conductivity fluid was obtained stationary solutions in the form of nonlinear periodic waves and kinks.

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References

Moffat G. Vozbuzdenie magnitnogo polja v provodjashej srede [Magnetic Field Generation in Electrically Conducting Fluids]. - M.: Mir, 1980. - 343p. (in Russian)

Zeldovitsh Ja.B., Ruzmajkin A.A., Sokolov D.D. Magnitnye polja v astrofizike [Magnetic Fields in Astrophysics]. - Izhevsk: Inst. Kopm.issl. RHD, 2006. - 384 p. (in Russian)

Vajnshtejn S.I. , Zeldovitsh Ja.B., Ruzmajkin A.A. Turbulentnoe dinamo v astrophisike [Turbulent Dynamo in Astrophysics]. – M.:Nauka, 1980. – 237p. (in Russian)

Vajnshtejn S.I. Magnitnye polja v kosmose [ Magnetic fields in Space]. - M.:Nauka, 1983. – 237p. (in Russian)

Parker Ju. Besedy ob elektritseskih i magnitnyh poljah v kosmose [Conversations on Electric and Magnetic Fields in Space]. - Izhevsk: Inst. Kopm.issl. RHD, 2010.- 208 p. (in Russian)

Krauze F., Pedler K.H. Magnitnaja gidrodinamika srednih polej i teorija dinamo [Mean-Field Magnetohydrodynamics and Dynamo Theory ]. - M.: Mir, 1984. – 314p. (in Russian)

Ruzmajkin A.A., Sokolov D.D., Shukurov A.M. Magnitnye polja galaktik [Magnetic fields of Galaxies]. - M.: Nauka, 1988. – 279p. (in Russian)

Sokolov D.D., Stepanov R.A., Frik P.G. Dinamo na puti ot astrofizitseskih modelej k labolatornomu eksperimentu[Dynamo: from an Astrophysical Model to Laboratory Experiments] // Usp. Fiz.Nauk. - 2014. - Vol. 184. - P.318-335. (in Russian)

Arnol'd V.I., Zel'dvich Ja.B., Ruzmajkin A.A., Sokolov D.D. Magnitnoe pole v dvizhushejsija provodashej zhidkosti [Magnetic Field in a Moving Conducting Fluid] // Uspehi matem. Nauk. - 1981. - No5. - P.220-221. (in Russian)

Arnol'd V.I. Evolutsija magnitnogo polija pod deijstviem perenosa I diffuzii [Evolution of Magnetic Field under the Action of Transfer and Diffusion ] // Uspehi matem. Nauk. - 1983. – No. 2. - P.225-227. (in Russian)

Grinspen H. Teorija vrashajushihsija zhidkostej [The Theory of Rotating Fluids]. Per. S angl. - Leningrad: Gidrometeoizdat, 1975. – 304p. (in Russian)

Reshetnyak M.Yu. Thermal Convection and the Dynamo during Rapid Rotation // Izvestija. Physics of the solid Earth.-2007. - Vol.43. - No.8. - P.642-652.

Pedloski Dj. Geofizicheskaija gidrodinamika v 2-h t. Per. s angl. [Geophysical Fluid Dynamics] - M.: Mir, 1984. (in Russian)

Petviashvili V.I., Pohotelov O.A. Uedinenye vihri v plasme i atmosfere [Solitary waves in Plasma and Atmosphere].- M.:Energoatomisdat, 1989. – 200p. (in Russian)

Aburdjanija G.D. Samoorganisatsia nelinejnyh vihrevyh struktur i vihrevoj turbulentnosti v dispergirujuscih sredah [Self-organization of Nonlinear Vortex Structures and Vortex Turbulence in Dispersive Media]. -M.:KomKniga, 2006. – 328p. (in Russian)

Kolesnichenko A.V., Marov M.Ja. Turbulentnost' i samoorganizatsija. Problemy modelirovanija kosmicheskikh i prirodnykh sred [Turbulence and self-organization. Problems of modeling space and natural environments]. - M.: BINOM, 2009. – 632p. (in Russian)

Onishenko O.G., Pohotelov O.A., Astafjeva N.M. Generatsyja krupnomasshtabnyh vihrej i sonalnykh vetrov v atmosferakh planet [Generation of Large-Scale Vortices and Zonal Winds in Planetary Atmospheres] // Usp. Fis. Nauk. - 2008. - Vol.178. - No. 6 - P. 605 - 618. (in Russian)

Nezlin M.V., Sneshkin E.N. Vikhri Rossby i spiral'nye struktury [Rossby Vortices and Spiral Structure ]. - M.: Nauka, 1990. – 240p. (in Russian)

Rudiger G. On the α - Effect for Slow and Fast Rotation // Astron. Nachr. - 1978. - Vol.299. - No.4. - P.217-222.

Steenbek M., Krause F. Vozniknovenie magnitnyh polej zvezd i planet v resul'tate turbulentnogo dvizhenija ih veshestv [The Origin of the Magnetic Fields of Stars and Planets as a Result of Turbulent Movement of their Substances] // Magnitnaja gidrodinamika. - 1967. - No.3. - P.19-44. (in Russian)

Moiseev S.S., Sagdeev R.Z., Tur A.V., Homenko G.A., Yanovsky V.V. Teorija vozniknovenija krupnomasshtabnykh struktur v gidrodiamitsheskoj turbulentnosti [The Theory of the Origin of Large-Scale Structures in Hydrodynamic Turbulence] // ZhETF. - 1983. - Vol.85. - Iss.6(12). - P.1979-1987. (in Russian)

Gilbert A. D., Frisch U., and Pouquet A. Geophys. //And Astrophys. Fluid Dyn.-1988.-Vol. 42.-P. 151-167.

Krause F., Rudiger G. On the Reynolds stresses in mean-field hydrodynamics. I. Incompressible homogeneous isotropic turbulence // Astron. Nachr. – 1974. Vol. 295. - P.93-99.

Chkhetiani O. G., Moiseev S. S., Petrosyan A. S., Sagdeev R. Z. The large scale stability and self-organization in homogeneous turbulent shear fow // Physica Scripta. - 1994. - Vol.49. - P.214–220.

Moiseev S.S., Rutkevith P.B., Tur A.V., Homenko G.A., Yanovsky V.V. Vortex dynamos in a helical turbulent convection // Sov.Phys.JETP.- 1988. – Vol. 67. – P. 294 -299.

Lypyan E.A., Mazurov A.A., Rutkevitch P.B., Tur A.V. Generation of large-scale vortices through the action of spiral turbulence of a convective nature // Sov.Phys.JETP. - 1992. -Vol. 75.- P.838-841.

Moiseev S.S., Oganjan O.R., Rutkevith P.B., Tur A.V., Homenko G.A., Yanovsky V.V. Vikhrevoe dinamo v spiral'noj turbulentnostju [Vortex Dynamo in Helical Turbulence] - Kiev: Naukova dumka. Sb.: Integriruemost i kinetitcheskie uravnenija dlja solitonov, 1990. - P.280-382. (in Russian)

Levina G.V., Moiseev S.S., Rutkevitch P.B. Hydrodynamic alpha-effect in a convective system // Advance in Fluid Mechanics.-2000.-Vol. 25.-P. 111.

Zimin V.D., Levina G.V., Moiseev S.S., Tur А.V. Vozniknovenie krupnomasshtabnych struktur pri turbulentnoy konvektsij v podogrevaevom snizu vrashajushemssja sloe [The Emergence of Large-Scale Structures under Turbulent Convection in a heated from below Rotating Layer] // Dokl. AN SSSR. - 1989. - Vol. 309. - P. 88-92. (in Russian)

Tur A.V., Yanovsky V.V. Large-scale instability in hydrodynamics with stable temperature stratification driven by small-scale helical force//arXiv:1204.5024 v.1 (physics.flu-dyn.)(2012).

Tur A.V., Yanovsky V.V. Non Linear Vortex Structure in Stratified Driven by Small- scale Helical Forse // Open Journal of Fluid Dynamics. - 2013. - Vol. 3 - P. 64-74.

Kopp M.I., Tur A. V., Yanovsky V. V. Krupnomasshtabnaja konvektivnaja neustojtchivost' v elektroprovodjashej srede s melkomasshtabnoj spiral'noj turbulentnostyju [Large-Scale Convective Instability in an Electroconducting Medium with Small Scale Helicity ] // ZhETF. - 2015. - Vol. 147. - Iss. 4. - P.846-866. (in Russian)

Rutkevich P. B. Equation for vortex Instability Caused by Convective Turbulence and Coriolis Force.// Sov.Phys. JETF. – 1993.- Vol. 77.- P.933.

Smith L. M. and Waleffe F. Transfer of Energy to Two-Dimensional Large Scales in Forced, Rotating Three-Dimensional Turbulence// Physics of Fluids.- 1999.- Vol. 11.- No. 6.- P.1608.

Smith L. M. and Waleffe F. Generation of Slow Large Scales in Forced Rotating Stratified Turbulence // Journal of Fluid Mechanics. - 2002. - Vol.451. - P.145 -168.

Berezin Y. A. and Zhukov V. P. An Influence of Rotation on Convective Stability of Large Scale Distorbances in Turbulent Fluid // Izv. AN SSSR. Mech. Zhidk. Gaza. - 1989. - No. 4. - P.3.

Kitchatinov L.L., Rudiger G., and G.Khomenko. Large –scale vortices in rotating stratified disks // Astron. Astrophys. - 1994. -Vol.287. - P.320-334.

Frishe U., She Z.S., Sulem P.L. Large Scale Flow Driven by the Anisotropic Kinetic Alpha Effect // Physica 28D. - 1987. - P. 283 - 291.

Druzhinin O.A., Homenko G.A. Nelinejnaja teorija gidrodinamitsheskogo alfa-effekta v szhimaemoj srede i obratny kaskad energii [Nonlinear Theory of Hydrodynamic Alpha-Effect in the Compressible Fluid and the inverse Energy Cascade]. – Kiev: Naukova dumka. Tr. Mezhdunarodnoj konf.: Nelinejnye i turbulentnye protsessy v fizike, 1989. - Vol.2. - P.83 -86. (in Russian)

Rutkevitch P.B., Sagdeev R.Z., Tur A.V., Yanovsky V.V. Nonlinear dynamic theory of the α -effect in compressible fluid. - Kiev: Naukova dumka. Proceeding of the IV Intern.Workshop on Nonlinear and Turb. Pros.in Physics, 1989.

Kopp M., Tur A., Yanovsky V. The Large Scale Instability in Rotating Fluid with Small Scale Force // Open Journal of Fluid Dynamics.- 2015.- Vol. 5.- P. 128-138.

Dolginov A.Z., Urpin V.A. Termomagnitnaja neustojtchivost' neodnorodnoj plazmy [Thermomagnetic Instability of an Inhomogeneous Plasma] // ZhETF. - 1978. - Vol.77. - P.1921-1932. (in Russian)

Published
2017-05-13
Cited
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How to Cite
Kopp, M., Tur, A., & Yanovsky, V. (2017). NONLINEAR DYNAMO IN A ROTATING ELECTRICALLY CONDUCTING FLUID. East European Journal of Physics, 4(1), 4-27. https://doi.org/10.26565/2312-4334-2017-1-01