Hydromagnetic stability of some non-dissipative flows subject to non-axisymmetric disturbances
Tóm tắt
We study the linear stability of nondissipative flow of an electrically conducting fluid subject to non-axisymmetric disturbances in the following cases: (i) the radial flow of an incompressible fluid between two concentric porous circular cylinders in the presence of a radial magnetic field and (ii) axial flow of a compressible fluid between two concentric circular cylinders permeated by a helical magnetic field (0,B
0θ(r),B
0z) in a cylindrical coordinate system. It is shown that in case (i), the flow is stable if the Alfvén velocity based on the undisturbed radial magnetic field exceeds the radial velocity due to suction or injection at the cylinder surfaces. In case (ii), it is found that under certain conditions the complex wave speed for an unstable mode lies within a circle of diameterW
max-W
min, whereW
max andW
min are the maximum and minimum values of the axial velocity in the flow region. In the presence of a purely axial magnetic field, however, the complex wave speed for an unstable mode always lies within the above circle.
Tài liệu tham khảo
Alfvén, H.: 1961,Astrophys. J. 133, 1049.
Barston, E. M.: 1980.Int. J. Eng. Sci. 18, 477.
Chandrasekhar, S.: 1961,Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford.
Chang, T. S. and Sartory, W. K.: 1967,J. Fluid Mech. 27, 65.
Dandapat, B. S. and Gupta, A. S.: 1975,Quart. Appl. Math. 33, 182.
Ganguly, K. and Gupta, A. S.: 1985,J. Math. Anal. Appl. 105 (in press).
Ganguly, K., Bhattacharyya, S. N., and Gupta, A. S.: 1985,Int. J. Eng. Sci. (in press).
Globe, S.: 1959,Phys. Fluids 2, 404.
Howard, L. N. and Gupta, A. S.: 1962,J. Fluid Mech. 14, 463.
Lindberg, L. and Jacobsen, C.: 1961,Astrophys. J. 133, 1043.
Lucas, R. J.: 1981,Int. J. Eng. Sci. 19, 819.
Michael, D. H.: 1954,Mathematika 1, 45.
Rayleigh, J. W. S.: 1916,Proc. Roy. Soc. London Ser. A93, 148.