Though a hydrodynamic model of the atmosphere allows both slow waves whose propagation speed is comparable to the wind speed and fast waves whose propagation speed is comparable to sound speed, the last ones practically are not observed in the large scale of the dynamics of the real atmosphere, i.e. mapped on meteorological charts. In order to explain this fact, we have considered the barotropic model in which the only slow and fast waves are the quasi-geostrophic Rossby waves and the ageostrophic Lamb waves, respectivelly. If the mechanism of the atmospheric turbulence is additionally included into the model, then 3 factors (the Earth size, the angular velocity of its rotation about its axis and the propagation velocity of a signal in the atmosphere) provide a much faster attenuation of the fast waves of all lengths in comparison with the slow waves. The mechanism of geostrophic adjustment is very effective due to a mean value of the vertical mixture coefficient in the atmosphere. While the lifetime of the Rossby waves is about 7 days, the lifetime of the synoptic scale Lamb waves is some tens less.
Hydrodynamic modelling; Atmospheric waves; Geostrophic balance
