Compressibility effects on outflows in a two-fluid system. 1. Line source in cylindrical geometry

A two-dimensional line source outflow is considered, in which the evolution of a sharp interface separating an incompressible fluid from a bounding weakly compressible gas is analysed. Linear theory is applied, assuming that anisotropies in the source outflow are small, to develop an approximate solution for the interfacial evolution. The simplest solutions to the governing linearised equations require the presence of a high-order velocity singularity at the location of the line source. A spectral method is also developed to capture the nonlinear behaviour of the flow; after some finite time, curvature singularities are found to develop on the interface. Comparisons are made between the stability of the interface and its analogue which separates two incompressible fluids. It is found that when the bounding fluid is weakly compressible rather than incompressible, the stability of the interface is significantly increased.