Steady Vortex Sheets in Presence of Surface Tension

Abstract

Abstract In this paper, we construct a new class of uniformly rotating vortex sheets arising as perturbations of the circular configuration within the Kelvin–Helmholtz model for two incompressible fluids of equal density, with surface tension effects taken into account. Despite the fundamental importance of the problem, few results are available on the long-time dynamics, due to the strong instability inherent in the Kelvin–Helmholtz mechanism. We carry out a detailed bifurcation analysis and construct families of nontrivial rotating solutions that bifurcate from the circular state when either the rotational speed or the surface tension coefficient is varied. The stationary branches obtained by varying the mean vorticity follow from the same analysis through the scaling symmetry of the equations.