Planar Rayleigh-Taylor instabilities: outflows from a binary line-source system

Rayleigh-Taylor instabilities occur when a light fluid lies beneath a heavier one, with an interface separating them. Under the influence of gravity, the two fluid layers attempt to exchange positions, and as a result, the interface between them is unstable, forming fingers and plumes. Here, an analogous problem is considered, but in cylindrical geometry. Two line sources are present within an inner region of lighter fluid, and each of them has an inwardly directed gravity field. The surrounding fluid is heavier and is pushed outward by the light inner fluid ejected from the two sources. Nonlinear inviscid solutions are calculated and compared with the results of a linearized inviscid theory. In addition, the problem is formulated as a weakly compressible viscous outflow and modeled with Boussinesq theory. It is found that vorticity is generated in the viscous interfacial zone but that overturning plumes do not develop. However, the solution growth is highly sensitive to initial conditions.