Surface Excitations of a Compressible Cylindrical Liquid

The stability of an infinitely long, inviscid but compressible liquid jet under sinusoidal disturbances of the surface, still assumed to be sharp, is considered. This extends Rayleigh's theory. We show that despite compressibility the unstable region is /.> kc = 2na (/. wavelength, a radius) as Rayleigh's criterion for incompressible liquids states. The character of the unstable long wavelength mode changes with compressibility showing a critical onset if the inverse compressibility is only half the surface pressure. The maximum decay rate increases with compressibility and the most unstable wavelength increases too. An infinity of sound-like modes exists; their dispersion relations and flow fields are also given.