垂直磁場によって変形された2次元Couette流の安定性

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概要

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• The hydromagnetic stability against small disturbances is investigated of the plane laminar motion of an electrically conducting fluid between parallel planes in relative motion in the presence of a transverse magnetic field. It is already established that the ordinary hydro-dynamical plane Couette flow is ultimately stable for all Reynolds numbers so far as the small disturbances are concerned. On the other hand, it is known that the effect of a magnetic field on the stability of laminar flows of an electrically conducting fluid is generally of stabilizing nature. Therefore, it may be natural to suppose that the modified plane Couette flow is also stable against small disturbances for all Reynolds numbers. Present investigation reveals, however, that this conjecture is not the case. In fact, it is found that the disturbances are amplified for a certain range of Reynolds number if Hartmann number M is larger than about 4. The final aim of the present investigation is to obtain the curve of neutral stability in the (α, R_e)-plane (α, the wave-number of the disturbance; R_e, Reynolds number) and to find the critical Reynolds number of the flow for various Hartmann numbers. At the present stage, however, the calculation has been carried out only for the disturbance of vanishing wave-number α=0. It has been found that there exist two asymptotic branches of the neutral curve if M>3.91. Both branches behave like α ∝R_e^<-1> as α→0. The more detailed account of the complete work will be published elsewhere.

• 宇宙航空研究開発機構の論文

著者

• 角谷 典彦

  京都大学理学部物理学教室

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