Journal of University of Chinese Academy of Sciences >
Magnetohydrodynamic instability of electrically conducting fluid between parallel plates
Received date: 2012-06-11
Revised date: 2012-09-19
Online published: 2012-09-19
Instability of an electrically conducting fluid between two parallel plates, affected by an imposed transversal magnetic field, is numerically investigated by Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. Details of instability are analyzed by solving the generalized Orr-Sommerfeld equation to determine the wavenumbers, growth rates, and spatial shapes of the eigenmodes.
ZAKIR Hussain , LIU Chan , NI Ming-Jiu , ZHANG Nian-Mei . Magnetohydrodynamic instability of electrically conducting fluid between parallel plates[J]. Journal of University of Chinese Academy of Sciences, 2013 , 30(3) : 304 -310 . DOI: 10.7523/j.issn.1002-1175.2013.03.004
[1] Lin C C. The theory of hydrodynamic stability[M]. Cambridge: Cambridge Uni Press, England, 1955: 1-75.
[2] Lock R C. The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field[J]. Proc Roy Soc Lond, 1955, A 233: 1005.
[3] Dahlburg R B, Zang T A, Montgomery D, et al. Viscous resistive magnetohydrodynamic stability computed by spectral techniques[J]. Proc Matl Acad Sic USA, 1983, 80:5798-5802.
[4] Hu J, Ben Hadid H, Hennry D. Linear stability analysis of Poiseuille-Rayleigh-Benared flow in binary fluid with soret effect[J]. Phys Fluid, 2007, 19:034101-12.
[5] Taghavi S M, Khabazi N, Sadeghy K. Hydromagnetic linear instability analysis of Giesekus fluids in plane poiseuille flow[J]. Commun Nonlinear Sic Num Sim, 2009,14:2046-2055.
[6] Bühler L. Instability in quasi-two-dimensional magnetohydrodynamic flow[J]. Fluid Mech, 1996, 326: 125-150.
[7] Müller U, Bühler L. Magnetofluiddynamics in channels and containers[M]. Berlin: Springer, 2001.
[8] Vorobev A, Zikanov O. Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field[J]. Fluid Mech, 2007, 574:131-154.
[9] Fakhfakh W, Kaddeche S, Henry D, et al. Selective control of Poiseuille-Rayleigh-Bénard instabilities by a spanwise magnetic field[J]. Phys Fluids,2010, 22:0341031-10.
[10] Priede J, Aleksandrova S, Molokov S. Linear stability of Hunts flow[J]. Fluid Mech, 2010, 649:115-134.
[11] Orszag S A. Accurate solution of the Orr-Sommerfeld stability equation[J]. Fluid Mech, 1971, 50:689-703.
[12] Takashima M. The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field[J]. Fluid Dynamics, 1995, 17:293-310.
[13] Hamming R W. Numerical methods for scienentist and engineers[M]. New York: McGraw-Hill, 1962.
[14] Fox L, Parker I B. Chebyshev polynomials in numerical analysis[M]. Oxford: Oxford University Press, 1968.
[15] Wilkinson J H. The algebraic eigenvalue problem[M]. Oxford: Oxford Univ Press, London, 1965.
[16] Gary J, Helgason R. A matrix method for ordinary differential equation[J]. Comp Phys, 1970, 5:159-205.
[17] Drazin P G, Reid W H. Hydrodynamic Stability[M]. Cambridge: Cambridge Univ Press, UK, 1981.
[18] Watanabe T. Magnetohydrodynamic stability of boundary layers along a flat plate in the presence of a transverse magnetic field[J]. Z Angew Math Mech (ZAMM), 1978, 58:555-560.
[19] Marsden J E. Stability and transition on shear flow[M]. New York: Springer-Verlag, 1-555.
/
| 〈 |
|
〉 |