The stability analysis of an inflexion-free velocity profile and its application to the night-time boundary layer in the atmosphere

The characteristics of waves excited in a stratified shear flow with a velocity profile monotonically increasing above the ground are calculated numerically. It is shown that unstable modes exist when the Brunt-Vaisala frequency of the ambient atmosphere decreases sufficiently fast with height. Their growth rates as a function of the horizontal wavelength and the local Richardson number are given, and a comparison between them and experimental data obtained for the night-time-boundary layer of the Earth's atmosphere is carried out. Finally, the characteristics of the singular neutral modes that the system can support are presented.