TEMPORAL AND SPATIAL INSTABILITY OF AN INVISCID COMPOUND JET

This paper examines the linear hydrodynamic stability of an inviscid c ompound jet. We perform the temporal and the spatial analyses in a uni fied framework in terms of transforms. The two analyses agree in the l imit of large jet velocity. The dispersion equation is explicit in the growth rate, affording an analytical solution. In the temporal analys is, there are two growing modes, stretching and squeezing. Thin film a symptotic expressions provide insight into the instability mechanism. The spatial analysis shows that the compound jet is absolutely unstabl e for small jet velocities and admits a convectively growing instabili ty for larger velocities. We study the effect of the system parameters on the temporal growth rate and that of the jet velocity on the spati al growth rate. Predictions of both the temporal and the spatial theor ies compare well with experiment.