The Instability of a Round Jet Surrounded by an Annular Shear Layer

A linear stability analysis of the large-scale structure of a round jet surrounded by an annular shear layer is presented. The study is limited to the developing region near the jet nozzle in the limit Re→∞. The radial dependence of the amplitudes of growing disturbances are examined in order to illustrate the extent to which the disturbances penetrate into the jet and its surroundings. The region influenced by a disturbance is found to be directly proportional to the wavelength of the disturbance. Disturbance measurements made on the jet centerline tend to select for long wavelength disturbances, while measurements made in the shear layer tend to select for short wavelength disturbances. When the shear layer thickness is small compared with the jet radius, the wavelength of the most amplified disturbance scales with the shear layer thickness. As the shear layer thickness increases, this scaling quickly breaks down. This change in scaling appears to be responsible for the transition between the “ripples” which occur near the jet nozzle and the “puffs” which are observed further downstream. Amplified disturbances exhibit a phase lag across the shear layer, which may account for the spade-like structures evident in flow visualizations of turbulent jets.