Power spectrum of a gravity wave propagating in a shearing background wind

We re-analyze the effect on the spectral tail of a gravity wave propagating in a shearing background. The contribution to the spectrum of horizontal wind perturbations for low vertical wavenumbers comes from the Doppler shifting with a -1 slope and for high wavenumbers from the leakage effect with slopes ranging between -4 to -2. If leakage is not present, it becomes necessary to consider the termination of the wave in order to account for the spectral tail. We show that the decreasing of the wave amplitude when the overturning starts, leads to a spectral slope of -3, and an amplitude proportional to N (the square of the Brünt Väisälä frequency).