Abstract
The stability and characteristics of Kelvin-Helmholtz waves in an atmosphere that may be saturated over some of its height are investigated analytically and numerically. It is shown that, if there is a temperature jump at the interface, the Wegener hypothesis, i.e., the assumption that stability boundary curves are loci of neutral waves travelling with phase velocity equal to the mean of the velocities of the regions above and below the discontinuity, is invalid. Instead, the stability boundary corresponds to the singular neutral modes with phase speed equal to the velocity in one or the other layer, depending on the sign of the temperature jump and the presence of saturation. Furthermore, the effect of saturation on the stability is found to be substantial. For the common case of a shallow saturated layer adjacent to the interface, the system is shown to behave essentially as if the temperature jump were smaller by an amount proportional to the mixing ratio and thickness. Finally, the validity of the Boussinesq approximation is examined and is found to be in error by less than 1% for horizontal wavelengths between 10 and 104 m.
