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Письма в ЖЭТФ, 2003, том 77, выпуск 12, страницы 788–793 (Mi jetpl2842)  

Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)

Variational principle in canonical variables, Weber transformation and complete set of the local integrals of motion for dissipation–free magnetohydrodynamics

A. V. Kats

Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine

Аннотация: The intriguing problem of the «missing» MHD integrals of motion is solved in the paper, i.e., analogs of the Ertel, helicity and vorticity invariants are obtained. The two latter were discussed earlier in the literature only for the specific cases, and Ertel invariant is first presented. The set of ideal MHD invariants obtained appears to be complete: to each hydrodynamic invariant corresponds its MHD generalization. These additional invariants are found by means of the fluid velocity decomposition based on its representation in terms of generalized potentials. This representation follows from the discussed variational principle in Hamiltonian (canonical) variables and it naturally decomposes the velocity field into the sum of «hydrodynamic» and «magnetic» parts. The «missing» local invariants are expressed in terms of the «hydrodynamic» part of the velocity and therefore depend on the (non–unique) velocity decomposition, i.e., they are gauge–dependent. Nevertheless, the corresponding conserved integral quantities can be made decomposition–independent by the appropriate choosing of the initial conditions for the generalized potentials. It is also shown that the Weber transformation of MHD equations (partially integration of the MHD equations) leads to the velocity representation coinciding with that following from the variational principle with constraints. The necessity of exploiting the complete form of the velocity representation in order to deal with general–type MHD flows (non–barotropic, rotational and with all possible types of breaks as well) in terms of single–valued potentials is also under discussion. The new basic invariants found allows one to widen the set of the local invariants on the basis of the well–known recursion procedure.

Полный текст: PDF файл (174 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Journal of Experimental and Theoretical Physics Letters, 2003, 77:12, 657–661

Реферативные базы данных:

Тип публикации: Статья
PACS: 04.20.Fy, 47.10.+g
Поступила в редакцию: 28.05.2003
Язык публикации: английский

Образец цитирования: A. V. Kats, “Variational principle in canonical variables, Weber transformation and complete set of the local integrals of motion for dissipation–free magnetohydrodynamics”, Письма в ЖЭТФ, 77:12 (2003), 788–793; JETP Letters, 77:12 (2003), 657–661

Цитирование в формате AMSBIB
\RBibitem{Kat03}
\by A.~V.~Kats
\paper Variational principle in canonical variables, Weber transformation and complete set of the local integrals of motion for dissipation--free magnetohydrodynamics
\jour Письма в ЖЭТФ
\yr 2003
\vol 77
\issue 12
\pages 788--793
\mathnet{http://mi.mathnet.ru/jetpl2842}
\transl
\jour JETP Letters
\yr 2003
\vol 77
\issue 12
\pages 657--661
\crossref{https://doi.org/10.1134/1.1604415}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-3042797950}


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  • http://mi.mathnet.ru/jetpl2842
  • http://mi.mathnet.ru/rus/jetpl/v77/i12/p788

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Webb G.M., Dasgupta B., McKenzie J.F., Hu Q., Zank G.P., “Local and Nonlocal Advected Invariants and Helicities in Magnetohydrodynamics and Gas Dynamics: II. Noether'S Theorems and Casimirs”, J. Phys. A-Math. Theor., 47:9 (2014), 095502  crossref  zmath  isi  scopus
    2. Webb G.M., Dasgupta B., McKenzie J.F., Hu Q., Zank G.P., “Local and Nonlocal Advected Invariants and Helicities in Magnetohydrodynamics and Gas Dynamics i: Lie Dragging Approach”, J. Phys. A-Math. Theor., 47:9 (2014), 095501  crossref  zmath  isi  scopus
    3. Yahalom A., “Non-barotropic magnetohydrodynamics as a five function field theory”, Int. J. Geom. Methods Mod. Phys., 13:10 (2016), 1650130  crossref  mathscinet  zmath  isi  elib  scopus
    4. Yahalon A., “Simplified variational principles for non-barotropic magnetohydrodynamics”, J. Plasma Phys., 82:2 (2016)  crossref  isi  scopus
    5. Yahalom A., “A Conserved Local Cross Helicity For Non-Barotropic Mhd”, Geophys. Astrophys. Fluid Dyn., 111:2 (2017), 131–137  crossref  mathscinet  isi  scopus
    6. Yahalom A., “Non-Barotropic Cross-Helicity Conservation Applications in Magnetohydrodynamics and the Aharanov-Bohm Effect”, Fluid Dyn. Res., 50:1 (2018), 011406  crossref  mathscinet  isi  scopus
    7. Webb G., “Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws”, Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws, Lecture Notes in Physics, 946, Springer International Publishing Ag, 2018, 1–301  crossref  isi
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