A two-dimensional model was used to advect air parcels under the influence of a linear superposition of hydrostatic gravity waves. As wave amplitudes increased, vertically profiled wave perturbations became nonsinusoidal, producing increased spectral power at large wavenumbers M. At saturation amplitudes just before onset of convective instabilities, these tail spectra assumed universal M-3 shapes, similar to observed spectra in the atmosphere and oceans. ¿ 1999 American Geophysical Union