The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible atmosphere in the presence of a lower boundary are studied. A jump in the Brunt–Va¨isa¨la¨ frequency is introduced and the level at which this jump occurs is assumed to be different from the shear zone, to simulate sharp temperature discontinuities in the atmosphere. The results are compared with those of Pellacani, Tebaldi, and Tosi and Lindzen and Rosenthal. In the present configuration, new unstable modes with larger growth rates are found. The wavelengths of the most unstable gravity waves for the parameters pertaining to observed cases of clear air turbulence agree quite closely with the experimental values.