Three-dimensional flows of an inviscid incompressible fluid and an inviscid subsonic compressible gas are considered and it is demonstrated how the WKB method can be used for investigating their stability. The evolution of rapidly oscillating initial data is considered and it is shown that in both cases the corresponding flows are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. Analyzing the corresponding transport equations, a number of classical stability conditions are rederived and some new ones are obtained. In particular, it is demonstrated that steady flows of an incompressible fluid and an inviscid subsonic compressible gas are unstable if they have points of stagnation.

Magnetohydrodynamics and spectral theory. (Developments in electromagnetic theory and applications ; 4) Includes index. 1. Magnetohydrodynamics. 2. Spectral theory (Mathematics) I. Title. II. Series.

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The problem of translation symmetric stationary magnetohydrodynamic (MHD) flow is analyzed with respect to the different permitted flow regimes. A minimal set of equilibrium functions is constructed facilitating the complete explicit solution in the case of self-similar flow. It is found that limiting line and Alfvén singularities leads to a division in four distinct velocity regimes which cannot be connected by continuous flows. Instead, the three types of MHD shocks appear, enabling the system to pass from the high to the low speed regimes.

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