Periodic Starting Flows.

The behaviour of a two-dimensional shallow water periodic starting jet has been examined. The source mass flux varies sinusoidally. At the commencement of each cycle a vortex pair is impulsively spun up from rest. The vortices migrate away from their source at the head of a jet-like "tail" which is advecting mass and momentum into the vortex pair "cap". The flow was found to maintain symmetry about the jet axis in approximately 70 percent of the experiments. The investigation has demonstrated that the gross features of the flow can be described in terms of a characteristic length scale which is a function of the fluid density, the peak source momentum flux per unit depth and the flow cycle period. A semi-empirical theoretical model is developed to describe the growth and motion of the cap which was the dominant feature of the flow. The model allows for mass and momentum contributions to the cap from the unsteady jet. The unsteady jet is modelled independently using an integral formulation which assumes the jet structure to be self preserving. The cap and jet are initially coupled and behave like a starting jet. They become decoupled when the mean axial velocity at the base of the cap falls below the cap translational velocity. Subsequently the cap can be described as a turbulent vortex pair which is entraining ambient fluid, and is subject to the applied force of bottom frictional resistance. Laboratory experiments are described which examine the behaviour of the jet for various boundary conditions, including linearly varying depth and a uniform cross-flow. The gross features of the flow were recorded photographically using dye and surface particles as tracers. The effect of a cross-flow is to cause a dispersal of the vorticity in the upstream vortex, with the downstream vortex moving away from the source under the influence of the cross-flow and the self-induced motion of the image vortex across the boundary. The relevence of the vortex pair model to similar naturally occuring flows is discussed. In particular, it is considered that ebb tidal jets at coastal inlets behave in a like manner.