Maslov's method for stationary hydrostatic mountain waves

The ray solution for stationary hydrostatic mountain waves has a singularity along the vertical axis directly over the mountain. We use Maslov's method to improve the ray prediction. The ray solution is determined in the wave-number domain and is then mapped by inverse Fourier transform to give a spatial description of the wave field that approximates the linear solution over the mountain and elsewhere. We develop Maslov's method for a medium with a height-dependent mean wind and mean buoyancy, and we compare it with the traditional transform method and with the results of a numerical simulation.