  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.
