Parabolic equations for gravity and acousto-gravity waves

Parabolic equations for gravity and acousto-gravity waves are derived and i mplemented. The wave equations for these problems contain singularities at depths at which the buoyancy frequency equals the forcing frequency. One of the advantages of the parabolic equation solution is that it is easy to av oid numerical problems associated with the singularities. Some problems inv olve an infinite number of propagating modes. This artifact of neglecting v iscosity is handled by including stability constraints in the rational appr oximations used in the implementation of the parabolic equation. The parabo lic equation is tested for idealized problems involving surface, internal, and interface gravity waves. Parabolic equation solutions are also presente d for range-dependent problems involving internal waves in the ocean and ac ousto-gravity waves in the atmosphere. (C) 1999 Acoustical Society of Ameri ca. [S0001-4966(99)04906-1].