Instability of axisymmetric jet flows of a fluid having a radius-dependent density is investigated. The necessary condition for the existence of unstable waves depends not only on the velocity profile but also on the density gradient as well. Large density gradients, positive or negative, have stabilizing effects. The semicircle theorem for amplified waves is valid in this case. It is shown by considering the top-hat type velocity profile that the velocity-dependent semicircle bound is the best possible.

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