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Introduction

Observations of energy distribution of horizontal winds and temperature irregularities show an apparent universal behavior in the short vertical wavelength end of the spectrum. The observed shape appears to be independent of the altitude, place, and time (Van Zandt, 1982; Allen and Vincent, 1995). This fact has suggested the presence of physical processes which can act over the wave field leading it to a saturated form.

One of the most accepted theories associates the saturation of the waves belonging the spectral tail to interactions between different components of the wave field, specifically, Hines (1991) suggests that the Doppler shifting that suffers a wave propagating upon the wave field is the dominant process in the determination of the high wavenumber amplitudes.

However, the so developed theory can not reproduce the power law in the vertical wavenumber of the observed spectra. The asymptotic behavior obtained by Hines has a dependence. He argued that the high wavenumber part of the spectrum may be influenced by dissipative processes which could diminish the amplitudes.

The power law is directly related to the result obtained for a single gravity wave propagating in a shear flow (Pulido and Caranti, 2000). Hines used a similar law for a spectrum of gravity waves but to the best of our knowledge there is no work in the literature showing that these results for single waves can be extrapolated to continuous gravity wave spectra.

It is important to bear in mind the difference between the physical spectrum which is propagating upward, that we call spectrum, and the power spectrum resulting from the Fourier transform in a height interval which we call power spectrum (PS). For example, a single wave has a monochromatic spectrum in a fixed altitude while has a broad power spectrum when a height interval is analyzed.

In this preliminary work we show that when a continuous spectrum of gravity waves is propagating in a shear flow there are interference effects between the different components of the spectrum which alter the behavior observed for single waves, and a -3 power law results for the spectral tail. Our final objective is to include in the approach presented here the nonlinear advective interactions which are necessary to saturate the vertical power spectrum but not to give the observed shape of it as it is shown here.