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    Anatolii Tur

    9, avenue Colonel-Roche 31028 Toulouse cedex 4
    Center D’etude Spatiale Des Rayonnements, C.N.R.S.-U.P.S.


    Kopp M. I., Tur A. V., Yanovsky V. V.
    Nonlinear dynamo theory
    2015, Vol. 11, No. 2, pp.  241-266
    Using the asymptotic method of multiple scales construct nonlinear theory of large-scale structures in stratified conducting medium in the presence of small-scale oscillations of the velocity field and magnetic fields. Such small-scale stationary oscillations are generated by small external sources at low Reynolds numbers. The nonlinear system of equations describing the evolution of largescale structure of the velocity field and the magnetic fields are obtained. The linear stage of evolution leads to the well known instability. We study the equations of non-linear instability and its stationary solutions.
    Keywords: stratified conducting medium, nonlinear system of equations, instability, large scale structures, multiscale method
    Citation: Kopp M. I., Tur A. V., Yanovsky V. V.,  Nonlinear dynamo theory, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 2, pp.  241-266
    Berezovoj V. P., Tur A. V., Yanovsky V. V.
    Proposed simple model movements thin tubes under the influence of fluid flow. Was obtained a nonlinear equation for the string with the flow. Demonstrated the possibility of tube vibrations under the influence of fluid flow and criterion was found linear instability at a constant flow rate. In the condition where the linear instability conditions are violated the possibility of oscillations detected during the presence of small periodic oscillation of flow.
    Keywords: string, fluid flow, the equation of motion, instability, parametric resonance
    Citation: Berezovoj V. P., Tur A. V., Yanovsky V. V.,  Dynamics of thin tubes under the influence of fluid flow, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  183-194
    Kulik K. N., Tur A. V., Yanovsky V. V.
    In this work considered the motion of a point dipole vortex in circular domain occupied by an ideal fluid. The motion equations for a dipole vortex in an domain bounded by solid wall, are obtained. These equations have the Hamiltonian form. Integrability in the quadratures of the motion equations for a point dipole vortex in a circular domain is proved. The character movement vortex is discussed.
    Keywords: point dipole vortex, Hamiltonian, motion equations
    Citation: Kulik K. N., Tur A. V., Yanovsky V. V.,  The evolution point dipole vortex in a domain with circular boundaries, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 4, pp.  659-669

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