Abstract
The stability of vortex sheet roll-up is studied using a Lagrangian vortex method. We consider an initially unstable (Kelvin–Helmholtz) vortex sheet. During its nonlinear evolution, a perturbation is added to test it for a secondary instability. The growth of the perturbation depends on its phase and on the local strain rate. In the linear stage of this secondary instability, the dispersion relation is calculated. It is found that the growth rate and the cutoff wave number are fixed by the regularization parameter of the Birkhoff–Rott equation.
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