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Discussion

Using the nonlinear technique applied by Teitelbaum and Sidi (1976, 1979) to gravity shear waves we have shown that nonlinear terms becomes important when the amplitude of the wave is equal to the threshold given by the linear convective instability.

Nonlinear wave amplitudes are bounded everywhere even at the place where the transformation of coordinate fails. Moreover, the nonlinear maximum amplitude is equal to the linear maximum amplitude. What nonlinearities do is to ``move'' the maxima and minima to the same altitude which generate jumps in the density and temperature profiles. These surfaces where temperature jumps are located are not crossed by the flow, they move with it and because of that the wave should be quickly dissipated.

Therefore wave breaking is induced at the Hodges condition and it is unrealistic to assume a harmonic wave form above this condition altitude as it has been suggested by Dewan and Good. Temperature profiles fit better Chimonas' model because the wave is strongly attenuated at the contact surface.

From a spectral point of view, the power spectrum of a height interval can be divided into two parts one which has the contribution of the refraction and the other, the spectral tail, is composed by internal leakage. Therefore leakage is not only produced by Fourier transform contamination but also by physical processes involved in the wave termination.

Future work should take into account the dissipation effects and a time dependent scenario in order to give more realistic wave terminations and to address how the energy exchange with the surrounding is taking place. We think that these preliminary results shown in this work give a good starting point to improve the theoretical knowledge of these processes.

The conclusions extracted from this treatment are only valid for monochromatic waves and cannot be extrapolated to a broad spectrum where interference effects can alter the profile near the critical level and the presence of linear convective instabilities are not assured there, as it is shown in Pulido and Caranti (2000b).