Previous: Ext. Abst. Next: Nonlinear wave propagation Up: Ext. Abst.

Introduction

In a linear approach gravity waves propagating in a shear flow are strongly attenuated as they approach their critical levels. At this place the horizontal background velocity equals the horizontal phase speed and momentum of the waves will be transfered to the background flow [Booker and Bretherton, 1967].

Before the waves reach the critical level they have attained the Hodges condition where the mean buoyancy frequency () is equal to the buoyancy frequency perturbation generated by the wave. There the flow becomes convectively unstable [Hodges, 1967].

There are several speculations about how gravity waves break in the region between the first Hodges threshold and the critical level:

• In order to reproduce the observed vertical power spectrum (PS) Dewan and Good (1986) suggested that when a gravity wave has reached the Hodges condition, and its amplitude is increasing due to the lower density it encounter as it propagates upwards, the wave begins a continuous elimination of excess energy maintaining at every level the total buoyancy frequency at the threshold value. Sato and Yamada (1994) applied this idea to gravity waves in a shear flow allowing amplitude and wavelength changes.

• On the other hand Chimonas (1997) modeled wind irregularities with two extreme cases of wave termination, one oscillatory decay between the convective instability condition and the critical level and the other one with an abrupt termination at the Hodges condition. He concluded that the abrupt termination fits better the observed power spectra.

It is important to recognize that nonlinear distortions of the profile are crucial for a correct treatment of wave breaking. In this work we show that between the first instability condition and the critical level a contact surface arises. The temperature profile shows a discontinuity across this surface where fast conduction is expected resulting in a quick attenuation of the wave.

The consequences of these results are in disagreement with Dewan and Good's model, there is no harmonic wave form above the instability and the spectral tail amplitudes are due to internal leakage coming from the discontinuities in the temperature and wind profiles.