Unsteady Motion of Viscous Electrically Conductive Fluid Rotating in Half-Space Bounded by a Wall in the Presence of Medium Injection (Suction)

The study is devoted to studying motion of a viscous electrically conductive incompressible fluid, which initially rotates as a solid body with constant angular velocity together with a porous wall bounding it under the influence of suddenly appearing longitudinal oscillations of the wall. The wall forms an arbitrary angle with the axis of rotation. Unsteady flow is induced by longitudinal wall oscillations, injection (suction) of the medium directed perpendicular to the porous plate surface and by suddenly activated constant magnetic field directed on the normal to the plate. Solutions were constructed for velocity fields and fluid pressure. Induced magnetic field in the flow of electrically conductive fluid was determined. A number of particular cases of the wall motion were considered. Based on the results obtained, separate structures of the boundary layers adjacent to the wall were examined

Литература

[1] Slezkin N.A. Dinamika vyazkoy neszhimaemoy zhidkosti [Dynamics of viscous incompressible fluid]. Moscow, Gostekhizdat Publ., 1955.

[2] Thornley Cl. On Stokes and Rayleigh layers in a rotating system. Q. J. Mech. Appl. Math., 1968, vol. 21, no. 4, pp. 451--461. DOI: 10.1093/qjmam/21.4.451

[3] Gurchenkov A.A., Yalamov Yu.I. Non-steady-state flow at a porous plate with blowing (suction) of the medium. J. Appl. Mech. Tech. Phys., 1980, vol. 21, no. 4, pp. 488--491. DOI: 10.1007/BF00916482

[4] Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. 8. Elektrodinamika sploshnykh sred [Theoretical physics. Vol. 8. Electrodynamics of continuous media]. Moscow, Fizmatlit Publ., 2005.

[5] Alfwen H., Falthammar C.G. Cosmical electrodynamics. Fundamental principles. Claredon Press, 1963.

[6] Gurchenkov A.A. Dinamika zavikhrennoy zhidkosti v polosti vrashchayushchegosya tela [Dynamics of swirling fluid in a cavity of rotating body]. Moscow, Fizmatlit Publ., 2010.

[7] Gurchenkov A.A. The unsteady motion of a viscous fluid between rotating parallel walls. J. Appl. Math. Mech., 2002, vol. 66, no. 2, pp. 239--243. DOI: 10.1016/S0021-8928(02)00029-1

[8] Sivukhin D.V. Obshchiy kurs fiziki. T. 3. Elektrichestvo [General course of physics. Vol. 3. Electricity]. Moscow, Fizmatlit Publ., 2009.

[9] Xu C., Schuster E., Vazquez R., et al. Stabilization of linearized 2D magnetohydrodynamic channel flow by backstepping boundary control. Syst. Control Lett., 2008, vol. 57, no. 10, pp. 805--812. DOI: 10.1016/j.sysconle.2008.03.008

[10] Xu C., Schuster E., Vazquez R., et al. MHD channel flow control in 2D: Mixing enhancement by boundary feedback. Automatica, 2008, vol. 44, no. 10, pp. 2498--2507. DOI: 10.1016/j.automatica.2008.02.018

[11] Grigoriadisa D.G.E., Kassinos S.C., Votyakova E.V. Immersed boundary method for the MHD flows of liquid metals. J. Comput. Phys., 2009, vol. 228, no. 3, pp. 903--920. DOI: 10.1016/j.jcp.2008.10.017

[12] Chebotarev A.Yu. Control of magnetohydrodynamic flow in the formation of a magnetic field with a prescribed configuration. Comput. Math. Math. Phys., 2009, vol. 49, no. 11, pp. 1913--1920. DOI: 10.1134/S0965542509110086

[13] Stepanov R.A., Chupin A.V., Frik P.G. Screw dynamo in a torus. Vychislitel’naya mekhanika sploshnykh sred [Computational Continuum Mechanics], 2008, vol. 1, no. 1, pp. 109--117 (in Russ.).

[14] Noskov V., Denisov S., Frick P., et al. Magnetic field rotation in the screw gallium flow. Eur. Phys. J. B, 2004, vol. 41, no. 4, pp. 561--568. DOI: 10.1140/epjb/e2004-00349-8

[15] Rogachevskii I., Kleeorin N. Nonlinear theory of a "shear-current" effect and mean-field magnetic dynamos. Phys. Rev. E, 2004, vol. 70, no. 4, art. 046310. DOI: 10.1103/PhysRevE.70.046310

[16] Alexakis A., Mininni P.D., Pouquet A. Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence. Phys. Rev. E, 2005, vol. 72, no. 4, art. 46301. DOI: 10.1103/PhysRevE.72.046301

[17] Plunian F., Stepanov R. A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence. New J. Phys., 2007, vol. 9, art. 294. DOI: 10.1088/1367-2630/9/8/294

[18] Radier K.-H., Stepanov R. Mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow. Phys. Rev. E, 2006, vol. 73, no. 5, art. 056311. DOI: 10.1103/PhysRevE.73.056311

[19] Denisov S.A., Noskov V.I., Stepanov R.A., et al. Measurements of turbulent magnetic diffusivity in a liquid-gallium flow. JETP Lett., 2008, vol. 88, no. 3, pp. 167--171. DOI: 10.1134/S0021364008150058