LINEAR HYDRODYNAMIC INSTABILITY OF CIRCULAR JETS WITH THIN SHEAR LAYERS

A new asymptotic expansion well adapted to the linear stability study of compressible jets with thin shear layers is presented. The validity of the approximation is established by making numerical comparisons with solutions of the full cylindrical Rayleigh equation. In particular helical modes are shown to be asymptotically equivalent to three-dimensional disturbances of planar shear layers. When the Mach number is zero Squire's theorem is recovered in the limit of vanishing shear layer thickness, thereby establishing that the axisymmetric mode is necessarily the most unstable. Finally the asymptotic expansion is shown to converge on both the -alpha(i)(+) and -alpha(i)(-) branches of the absolute convective transition that takes place when a small back flow is added to the jet.