Nonlinear instability and break-up of separated flow

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Abstract
Unsteady effects in a separated recirculating eddy beneath a subsonic or supersonic mainstream are considered, with emphasis on nonlinear properties. The eddy is slender and predominantly inviscid, its length being comparable with, or less than, the chord of an airfoil, for instance. It is found, from the study of a family of integro-differential equations, that the planar eddy can break up nonlinearly within a finite time, causing an eruption into the main stream and setting up a subsequent Euler stage in the unsteady motion. Comparisons with recent experiments and further applications of the theory are discussed.