The unstable temporal development of axi-symmetric jets of incompressible fluid

We study the shear-driven instability, of Kelvin–Helmholtz type, that forms at the interface between a cylindrical jet of flowing fluid and its surroundings. The results of an infinitesimal-amplitude theory based on linearising the system about the undisturbed jet are given. A novel numerical model based on the Galerkin spectral method is developed and employed to simulate the non-linear development of the jet in the weakly-compressible Boussinesq regime. Representative results demonstrating the viability of this model are given, and are shown to agree with the linear analysis for small disturbances, but to develop cylindrical roll-up in the severely non-linear regime.