Magneto-Haydrodynamic Osciliating Flows and their applications

The project belongs to an active research direction - Vibrodynamics, which has been developed by the PI since 2004. It contains an efficient method of deriving asymptotic models with the use of the multi-scale approach, averaging method, and asymptotic analysis. An important achievement of Vibrodynamics is the Vladimirov's MHD-drift equation, which represents the classical MHD-equations averaged over imposed oscillations (see J. of Fluid Mech. 2012, vol.698, p.51). This project is devoted to the systematic study of these equations and related applications. Our plan is: (i) to understand the correspondence between Vladimirov's Vibrodynamics and Moffatt-Proctor-Hughes Mean-Field Theory; (ii) to analyze the presence of finite-time singularities in the vorticity and/or magnetic field; (iii) to establish the Hamiltonian structures and find all the conservation laws; (iv) to derive the Arnold-type nonlinear and linear stability criteria; (v) to apply Vladimirov-Moffatt analogy between effects of magnetic field and density stratification; (vi) to consider the linearized problems and to derive the Richardson-type stability and instability criteria; (vii) to clarify the possibility of the magneto-hydrodynamic dynamo including the Stokes-type dynamo; (viii) to apply MHD-drift equations to the problem of electromagnetic pumping; (ix) to apply it to the electromagnetic levitation and to the control of motions for rigid particles of various conductivity.

The project belongs to an active research direction - Vibrodynamics, which has been developed by the PI since 2004. It contains an efficient method of deriving asymptotic models with the use of the multi-scale approach, averaging method, and asymptotic analysis. An important achievement of Vibrodynamics is the Vladimirov's MHD-drift equation, which represents the classical MHD-equations averaged over imposed oscillations (see J. of Fluid Mech. 2012, vol.698, p.51). This project is devoted to the systematic study of these equations and related applications. Our plan is: (i) to understand the correspondence between Vladimirov's Vibrodynamics and Moffatt-Proctor-Hughes Mean-Field Theory; (ii) to analyze the presence of finite-time singularities in the vorticity and/or magnetic field; (iii) to establish the Hamiltonian structures and find all the conservation laws; (iv) to derive the Arnold-type nonlinear and linear stability criteria; (v) to apply Vladimirov-Moffatt analogy between effects of magnetic field and density stratification; (vi) to consider the linearized problems and to derive the Richardson-type stability and instability criteria; (vii) to clarify the possibility of the magneto-hydrodynamic dynamo including the Stokes-type dynamo; (viii) to apply MHD-drift equations to the problem of electromagnetic pumping; (ix) to apply it to the electromagnetic levitation and to the control of motions for rigid particles of various conductivity.