Wave structures in jets of arbitrary shape. I. Linear inviscid spatial instability analysis

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Abstract
Green function methods are used to give a practical form of the Rayleigh linear inviscid instability analysis for jets of arbitrary mean flow profile. Simple illustrations of the general methodology are given for vortex‐sheet and continuous‐velocity‐profile shear layers. Some of the numerical results for elliptic jets are compared with those previously obtained from solutions of Mathieu’s equation in elliptic cylindrical coordinates.