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Stability of dusty liquid at rest. Effect of vertical magnetic field. (English) Zbl 0599.76061

[For the former part see the summary above (Zbl 0599.76060)].
The stability of an incompressible, infinitely conducting dusty liquid of variable density in the presence of an applied vertical magnetic field is investigated by a linear analysis. It can be easily shown that the three- dimensional disturbance problem is equivalent to a two-dimensional disturbance problem. It is found that the stable stratification \((J>0)\) remains stable in the presence of vertical magnetic field but if \(S>| J| /\pi^ 2\) the unstable stratification \((J<0)\) which is unstable in the absence of magnetic field becomes stable. The region in which the values of \(\sigma_ r\) and \(\sigma_ i\) for an arbitrary unstable mode lie, is obtained in various situations. The effect of fine and coarse dust on the stability is discussed and discussion seems to confirm the results of Saffman.

MSC:

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows

Citations:

Zbl 0599.76060
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