Abstract
The nonlinear time evolution of a two-layer axisymmetric cylindrical sheet composed of inviscid incompressible fluids is studied. By numerically solving model equations derived on the basis of the thin-layer approximation, we examine the time evolution of a sheet that is disturbed from the state of axial uniform flow as one of the three eigenmodes in the linear stability analysis of this flow. If the initial eigenmode is unstable, the sheet breaks as the radius of its inner surface decreases to zero when the densities of two fluids are comparable, whereas it breaks as the minimum thickness of the layer of the lighter fluid decreases to zero when the difference in densities is sufficiently large. For initial disturbances of a linearly stable eigenmode with a large amplitude, the sheet breaks as the minimum thicknesses of either or both of the two layers decrease to zero, irrespective of the initial eigenmode and the ratios of densities, surface tension coefficients, and the thicknesses of the two layers.
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