The behavior of magneto-acoustic-gravity waves near the cusp resonance in a lossless, compressible, isothermal, stratified, electrically conducting, and uniformly magnetized atmosphere. I. Mode conversion approach

In the present paper the propagation of (internal) magneto-acoustic-gravity waves is analyzed in a compressible, isothermal, stratified, electrically conducting atmosphere that is permeated by a uniform, nearly horizontal magnetic field. The conversion, near the so-called cusp resonance of a long acoustic-gravity wave into a short slow magneto-acoustic wave, is demonstrated by means of boundary layer theory based on the smallness of the vertical component of the magnetic field. The magneto-acoustic wave subsequently carries the energy off upward, which in the limit of a horizontal magnetic field would be fed into the cusp resonance ad infinitum, This gives rise to singular fields. The scaling of the tendency toward singular behavior of a field quantity with the obliqueness of the magnetic field is discussed, as well as the partial reflection of the long acoustic-gravity wave.