Abstract
Flow visualization near the exit of a plane jet shows a small-amplitude disturbance whose wavelength is large relative to the jet shear layer thickness. Further downstream, in the transition region, concentrated regions of vorticity are observed which drive the flapping motion of the jet. These observations motivate an inviscid, two-dimensional model for the transitional region of the jet. Linear stability analysis of a piecewise-uniform shear layer model indicates that small-amplitude, long wavelength disturbances are unstable. Long wave theory shows that regions of high circulation convect downstream faster than regions of low circulation resulting in nonlinear steepening and that the rate of the steepening is directly proportional to the strength of the local shear. The long wave theory also shows that finite-amplitude sinuous disturbances at the jet centerline will grow linearly as they convect downstream. The results predict the steepening and growth of the jet centerline observed in the flow visualization.
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