The instability of a non-uniform vortex sheet

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Abstract
The classical Kelvin-Helmholtz problem of the instability of the vortex sheet between two uniform streams is extended to allow for non-uniformity in the streams. A small-wavelength approximation shows that the most unstable disturbances have a growth rate proportional to the greatest discontinuity of velocity at the vortex sheet. The solution for all wavelengths is found for two cases when the variation in the stream velocity is small compared with the stream velocity itself. One of these cases indicates that a transverse variation in the stream velocity can increase the instability for long wavelengths, but only to a small extent.

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