Isentropic advection by gravity waves:: Quasi-universal M-3 vertical wavenumber spectra near the onset of instability

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.