Stability of Hydromagnetic Kelvin-Helmholtz Discontinuity

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Abstract
The most general form of hydromagnetic Kelvin‐Helmholtz discontinuity in ideal incompressible fluids has been considered. The presence of surface tension on the surface of discontinuity and gravity is also assumed. The stability of the hydromagnetic flow of two uniform infinite streams with planar interface exhibiting this type of discontinuity, has been analyzed in detail. Two necessary and sufficient criteria for its stability have been obtained, in contrast to only one that is usually given. The stabilizing effect of magnetic field is strongly dependent on its discontinuity at the interface and its orientation relative to that of streaming. The consideration of the stability to a single mode of perturbation leads to the conclusion that this is dependent on the above mentioned factors, as well as the following ones. The effect of surface tension and gravity is dependent on the wavelength, while that of the magnetic field is dependent on the direction of propagation of perturbation.

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