LARGE-SCALE MAGNETIC AND VORTEX STRUCTURES IN A TURBULENT MEDIUM

  • V. V. Yanovsky Institute for Single Cristals, Nat. Academy of ScienceUkraine, Lenine Ave.60, Kharkov 31001,UkraineV.N. Karazin Kharkiv National UniversitySq. Svobody 4, Kharkiv, 61022 Ukraine https://orcid.org/0000-0003-0461-749X
  • 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
  • M. I. Kopp Institute for Single Cristals, Nat. Academy of ScienceUkraine, Lenine Ave.60, Kharkov 31001,Ukraine https://orcid.org/0000-0001-7457-3272
Keywords: dynamo theory, large-scale convective instability, Coriolis force, multiscale asymptotic expansions, α - effect, solitons, kinks

Abstract

The survey covers a main achievements in the field of dynamo theory. Applications of the model of turbulent convective dynamo to the problem of generation of a large-scale vortexes and magnetic structures in the solar photosphere are discussed. Investigated are the new models of the vortex dynamo in a rotating fluid with small-scale external force. The main results in these models are obtained by the method of multiscale asymptotic expansions. The results of numerical analysis of nonlinear equations of a magnetovortex dynamo in a stationary mode are provided. Solutions are found in the form of spiral kinks, periodic nonlinear waves and solitons, which are also considered in the survey.

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References

Petviashvili V.I., Pohotelov O.A. Uedinenye vihri v plasme i atmosfere.-M.:Energoatomisdat, 1989. - 200s.

Aburdjanija G.D. Samoorganisatsia nelinejnyh vihrevyh struktur i vihrevoj turbulentnosti v dispergirujuscih sredah. - M.:KomKniga, 2006. - 328s.

Onishenko O.G., Pohotelov O.A., Astafjeva N.M. Generatsyja krupnomasshtabnyh vihrej i sonalnykh vetrov v atmosferakh planet // Usp. Fis. Nauk. - 2008. - T.178. - No. 6 - S. 605 - 618.

Shmerlin B.Ja.,Kalashnik M.V. Konvektivnaja neustojtsivost' Releja v prisutstvie fasovih perehodov vlagi. Formirovanie krupnomasshtabnyh vihrej i oblatshnyh struktur // Usp. Fis. Nauk. - 2013. - T.183. - No. 5. - S.497 - 510.

Monin A.S. Vvedenie v teoriji klimata. - L.: Gidrometeoizdat, 1982. - 296s.

Tur A.V., Yanovsky V.V. Gidrodinamicheskie vihrevye struktury. - Har'kov: Institut monokristallov, 2012. - 290s.

Rolfs K. Lektsii po teoriji voln plotnosti. - M.: Mir, 1980. - 208s.

Morozov A.G., Hoperskov A.V. Fizika diskov. - Volgograd: Izd.-vo VolgGU, 2005. - 423s.

Nezlin M.V., Sneshkin E.N. Vikhri Rossby i spiral'nye struktury. - M.: Nauka, 1990. – 240s.

Moffat G. Nekotorye napravlenija razvitija turbulentnosti. Sovrem. Gidrodinamika. Uspehi i problemi. - M.: Mir,1984. - S.48 - 76.

Steenbek M., Krause F. Vozniknovenie magnitnyh polej zvezd i planet v resul'tate turbulentnogo dvizhenija ih veshestv // Magnitnaja gidrodinamika. - 1967. - No.3. - S.19-44.

Moffat G. Vozbuzdenie magnitnogo polja v provodjashej srede. - M.: Mir, 1980.- 343s.

Zeldovitsh Ja.B., Ruzmajkin A.A., Sokolov D.D. Magnitnye polja v astrofizike. - Izhevsk: Inst. Kopm.issl. RHD, 2006.- 384s.

Parker Ju. Besedy ob elektritseskih i magnitnyh poljah v kosmose. - Izhevsk: Inst. Kopm.issl. RHD, 2010.- 208s.

Krauze F., Pedler K.H. Magnitnaja gidrodinamika srednih polej i teorija dinamo. - M.: Mir,1984. - 314s.

Ruzmajkin A.A., Sokolov D.D., Shukurov A.M. Magnitnye polja galaktik. - M.: Nauka, 1988. - 279s.

Sokolov D.D., Stepanov R.A., Frik P.G. Dinamo na puti ot astrofizitseskih modelej k labolatornomu eksperimentu// Usp. Fiz.Nauk. - 2014. - T. 184. - S.318-335.

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.

Moiseev S.S., Sagdeev R.Z., Tur A.V., Homenko G.A., Yanovsky V.V. Teorija vozniknovenija krupnomasshtabnykh struktur v gidrodiamitsheskoj turbulentnosti // ZhETF. - 1983. - T.85. - Vyp.6(12). - S.1979-1987.

Petrosjan A.S. Dopolnitelnye glavy teorii turbulentnosti. Spiralnaja turbulentnost'. - M.: IKI RAN, 2013. - 60s.

Moiseev S.S., Rutkevith P.B., Tur A.V., Homenko G.A., Yanovsky V.V. Vikhrevoe dinamo v konvektivnoj srede so spiral'noj turbulentnostju // ZhETF. - 1988. - T.94. - Vyp.2. - S.144-153.

Smith L.M., 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.

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

Zimin V.D., Levina G.V., Moiseev S.S., Tur A.V. Vozniknovenie krupnomasshtabnykh struktur pri turbulentnoj konvektsii v podogrevaemom snizu vraschajuschemsja sloe // Dokl. AN SSSR.- 1989.-T. 309.- S. 88-92.

Rutkevich P. B. Equation for vortex Instability Caused by Convective Turbulence and Coriolis Force // JETF.- 1993.- Vol. 77.- P. 933-938.

Gershuni G.Z., Zhuhovickij E.M., Nepomnjashhij A.A. Ustojchivost' konvektivnyh techenij. - M.: Nauka, 1989. - 320s.

Getling A.V. Konvekcija Releja-Benara. Struktury i dinamika. - M.: Editorial URSS, 1999. - 248s.

Kuklin V.M. Rol' poglotchenija i dissipatsii energii i formirovanie prostranstvennykh nelinejnykh struktur v neravnovesnyh sredah // UFZh. - 2004. - T.4. - No. 1. - S.49-81.

Busse F.H. Generation of planetary by convection // Phys. Earth. Planet. Inter.- 1976.-Vol. 12.-P. 350-358.

Zang K.K., Busse F.H. Generation of magnetic fields by convection in a rotating spherical fluid shell of infinite Prandtl number // Phys.Eath.Planet.Inter. - 1990. - Vol. 59. - P.202-222.

Jones C.A. Convection-driven geodynamo models // Phil.Trans.Roy.Sos.Lond. - 2000. – Vol.A358. - P.873-897.

Glantzmaier G.A., Roberts P.H. Simulation the geodynamo // Contemp.Phys. - 1999. - Vol. 38. - P.269-288.

Braginskij S.I. O samovozbuzhdenii magnitnogo polja pri dvighenii khorosho provodjaschej zhidkosti // ZhETF. - 1964. - T. 47. - Vyp. 3. - S.1084-1098.

Matthews P.C. Dynamo action in simple convective flows // Proc. Roy. Soc. London. Ser.A. - 1999. - Vol. 455. - P.1829-1840.

Demircan A., Seehafer N.Dynamo in assymmetric square convection // Geophys. Astrophys. Fluid Dyn. - 2002 - Vol. 96. - P.461-479.

Podvigina O.M. Magnetic field generation by convective flows in plane layer // Eur. Phys J.B. - 2006 - Vol. 50. - P.639-652.

Podvigina O.M. Zavisimost' generatsii magnitnogo polija ot kineticheskogo chisla Prandtlia // Mater. Mezhdunar. konf. “Nelineinie zadachi teorii gidrodinamicheskoi ystoichivosti i turbulentnost'”. - M.: Mosk. yniv-teta. - 86s.

Arnol'd V.I., Zel'dvich Ja.B., Ruzmajkin A.A., Sokolov D.D. Magnitnoe pole v dvizhushejsija provodashej zhidkosti // Uspehi matem. Nauk. - 1981. – No.5. - S.220-221.

Arnol'd V.I. Evolutsija magnitnogo polija pod deijstviem perenosa I diffuzii // Uspehi matem. Nauk. - 1983. – No. 2. - S.225-227.

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.

Gertsenshtejn S.Ya., Chertovskikh R.A. Generatsija magnitnogo polja konvektivnymi techenijami vo vraschajuschemsja gorizontal'nom sloe // Mekhanika zhidkosti i gasa.-2008.-No. 2.- S.92- 101.

Chertovskikh R.A., Zheligovskikh V.A. Evoljutsija dlinnomasschtabnykh vozmuschenij statsionarnykh konvektivnykh MGD sostojanij // Proceedings of MSS-14. II. Large-scale instabilites in hydrodynamics and plasmas.- M.: IKI RAN, 2015.

Calkins M.A., Julien K., Tobias S.M., Aurnou J.M. A Multiscale Dynamo Model Driven by Quasi-geostrophic Convection // arXiv: 1502.03856v1(physics.geo-ph) 12 Feb 2015.

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.

Moiseev S.S., Oganjan K.R., Rutkevith P.B., Tur A.V., Homenko G.A., Yanovsky V.V. Vikhrevoe dinamo v spiral'noj turbulentnostju.- Kiev: Naukova dumka. Sb.: Integriruemost i kinetitcheskie uravnenija dlja solitonov, 1990. - S.280-382.

Kopp M.I., Tur A. V., Yanovsky V. V. Krupnomasshtabnaja konvektivnaja neustojtchivost' v elektroprovodjashej srede s melkomasshtabnoj spiral'noj turbulentnostyju // ZhETF. - 2015. - T. 147. - Vyp. 4. - S.846-866.

Levina G.V. Parametrizatsija spiralnoj turbulentnosti v chislennykh modeljakh intensivnykh atmosfernykh vikhrej // Dokl. RAN. -2006. - T. 411. - S.400-404.

Novikov E.A. Funktsionaly i metod sluchajnyh sil v teorii turbulentnosti //ZhETF. - 1964.-T.47. - Vyp.5(11). - S. 1919 - 1926.

Kljatskin V.I. Stohastitheskie uravnenija i volny v sluchajno-neodnorodnyh sredakh. - M.: Nauka, 1980. - 377s.

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.-Kiev: Naukova dumka. Tr. Mezhdunarodnoj konf.: Nelinejnye i turbulentnye protsessy v fizike, 1989. - T.2. - S.83 -86.

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.

Tshetiani O.G. Samoorganizatsija i turbulentnost v otrazhatelno- nesimmetritsnyh plazmenno-gidrodinamitseskih sredah. Diss. na soisk. utch. stepeni dokt. fiz.-mat. nauk. - Moskva, 1999. - 262 s.

Kopp M. I., Tur A. V., Yanovsky V. V. The Large Scale Instability and Nonlinear Vortex Structures in Obliquely Rotating Fluid with Small Scale Non Spiral Force// ВАНТ. - 2015. - No. 98. - S.264-269.

Shalit M.A. and Bellan P.M. Plasma current drive by injection of photons with helicity // Phys. of Fluids B.-1989. - Vol.1(12). - P. 2533-2534.

Sokolov I.V. Moment impul'sa elektromagnitnoj volny i generatsija magnitnykh polej v plazme //Usp. Fiz. Nauk.- 1991. - T. 161. - No. 10. - S.175-190.

Vajnshtejn S.I. Magnitnye polja v kosmose. - M.:Nauka, 1983. - 237s.

Dolginov A.Z., Urpin V.A. Termomagnitnaja neustojtchivost' neodnorodnoj plazmy // ZhETF. - 1978. - T.77. - S.1921-1932.

Montgomery D., Chen H. Turbulent amplification of large-scale magnetic fields // Plasma Physics and Controlled Fusion. - 1984. - Vol. 26. - No. 10. - P. 1199 -1210.

Kopp M.I., Tur A.V., Yanovsky V.V. Nelinejnaja teorija dinamo // Nelinejnaja dinamika. – 2015. - T.11. - No.2. - S.241-266.

Kaplan S.A., Pikelner S.B., Tsytovich V.N. Fizika plazmy solnechnoj atmosfery.-M.: Nauka, 1977.- 256s.

Brandt P.N., Sharmet G.B., Ferguson S., Shine R.A., Tarbell T.D., Title A.M. Vortex flow in the solar photosphere // Nature. - 1988. - Vol. 335. - P. 238-240.

Grinspen H. Teorija vrashajushihsija zhidkostej. Per. s angl. - Leningrad: Gidrometeoizdat, 1975. - 304s.

Kolesnichenko A.V., Marov M.Ja. Turbulentnost' i samoorganizatsija. Problemy modelirovanija kosmicheskikh I prirodnykh sred. - M.: BINOM, 2009. - 632s.

Lahin V.P. Neustojchivosti i volny vo vraschajuschejsja plazme i turbulentnaja generatsija reguljarnykh struktur. Diss. na soisk. utch. stepeni dokt. fiz.-mat. nauk. - Moskva, 2013. - 257 s.

Pedloski Dj. Geofizicheskaija gidrodinamika v 2-h t. Per. s angl. - M.: Mir, 1984.

Sommeria J., Meyers S.P., Swinney H.L. Laboratory simulation of Jupiters Great Red Spot // Nature ( London). - 1988. - Vol.331. - P.689-693.

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.

Bronsteyjn I.N., Semendjaev K.A. Spravotchnik po matematike dlja inzhenerov i utchatshihsja vtuzov. - M.: Nauka, 1981. - 718s.

Published
2016-04-23
Cited
How to Cite
Yanovsky, V. V., Tur, A. V., & Kopp, M. I. (2016). LARGE-SCALE MAGNETIC AND VORTEX STRUCTURES IN A TURBULENT MEDIUM. East European Journal of Physics, 3(1), 4-22. https://doi.org/10.26565/2312-4334-2016-1-01