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.