Fluid Dynamics

, Volume 1, Issue 1, pp 1–4 | Cite as

Flow stability of a conducting liquid flowing down an inclined plane in the presence of a magnetic field

  • Yu. P. Ladikov
Article

Abstract

The stability of a steady flow of incompressible, conducting liquid down an inclined plane in the presence of longitudinal and transverse magnetic fields is studied. Solutions of the linearized magnetohydrodynamic equations with corresponding boundary conditions are found on the assumption that the Reynolds number Rg and the wave number α are small. It is shown that the longitudinal magnetic field plays a stabilizing role. It is known [1] that the flow of a viscous liquid over a vertical wall is always unstable. In this article it is shown that the instability effect at small wave numbers may be eliminated if the longitudinal magnetic field satisfies the conditions found. The case when the Alfvén number and the wave number are small and the Reynolds number is finite is also examined.

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References

  1. 1.
    Yih Chia Shun, “Stability of liquid flow down an inclined plane,” Phys. Fluids, vol. 6, no. 3, p. 321–334, 1963.Google Scholar
  2. 2.
    K. B. Pavlov, “Stability of plane Couette flow in the presence of a magnetic field,” in: Problems of Magnetohydrodynamics and Plasma Dynamics [in Russian], Iad. AN Latv. SSR, Riga, 1961.Google Scholar

Copyright information

© The Faraday Press, Inc. 1967

Authors and Affiliations

  • Yu. P. Ladikov
    • 1
  1. 1.Orsk

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