Compressibility effects on outflows in a two-fluid system. 2. Point source in spherical geometry

Abstract

Fluid outflow from a point source into a surrounding fluid of different density is considered. A sharp interface separates the two fluids, and its mean radius increases with time due to the mass produced by the source. The inner fluid is incompressible and inviscid, but the outer fluid is weakly compressible and is modelled using a Boussinesq approximation. A linearized theory is presented, and it assumes that disturbances to the overall outflow remain small in amplitude. A spectral scheme for solving the non-linear problem is discussed. The results demonstrate that compressibility acts to suppress the Rayleigh–Taylor type instability of the interface, which would occur if both fluids were incompressible. In addition, the compressibility of the outer fluid forces the source within the inner incompressible fluid to behave in a more complicated manner while still preserving the overall ejected mass flux. This is confirmed in both the linearized and non-linear solutions.