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On the properties of hydromagnetic waves in the vicinity of critical levels and transition layers. (English) Zbl 0657.76087

The propagation of magnetosonic-gravity waves in the solar atmosphere is analyzed. This problem is reduced to the study of the ordinary differential equation (*) \(W''+P(z)W'+Q(z)W=0\) which has singularities when the coefficients P(z) and Q(z) are singular at some point \(z=z_ c\). Such point marks a critical level of the atmosphere. It is shown that there exist three types of critical levels for the logarithmic singularity of solutions of the equation (*). These types correspond to the evanescense, mode conversion and reflection of waves at the critical level.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76E20 Stability and instability of geophysical and astrophysical flows
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
76M99 Basic methods in fluid mechanics
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