Spectral differences between a single gravity shear wave and a continuous superposition of modes

A continuous superposition of gravity waves, propagating upward in a shearing background wind, is analyzed. Starting from the gravity wave equations, it is proven, analytically and numerically, that a uniform spectrum has a resultant Doppler-shifted power spectrum with a ?3 power law at large vertical wavenumber contrasting with the ?1 power law that characterizes the power spectrum of the monochromatic wave perturbation profile. The preliminary results presented here show that, assuming conservative propagation (no dissipative processes), the Doppler shifting effect can account for observations.