Abstract
The Kelvin-Helmholtz problem deals with the stability of superposed fluids in relative motion. For a basic discontinuity in the velocity of 2U and a constant Brunt-Vaisala frequencyN it has been found that in the Boussinesq approximation small perturbations with a horizontal wavenumberk, such thatk 2>N 2/2U 2, are unstable. When the fluid is assumed to be compressible and taking into account the variation of the density in all the equations we find that there are also instabilities fork 2<N 2/2U 2. However, the growth rate of these instabilities is small. The horizontal phase velocities of the instabilities are also different from those obtained in the Boussinesq approximation. But again the difference is small. On the other hand, in the hydrostatic approximation, which takes into account the compressibility too, all instabilities disappear.
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