Starting jets in shallow waters are produced by exchange across an inlet between water of different depths. The flow in the jet is supercritical when the depth difference across the inlet is sufficiently large so that the jet is regulated by the critical flow at the inlet. The flow in the jet becomes subcritical when the flow at the inlet is drowned by the downstream water. The vorticity and dilation structures of the jets including shock waves in the jets and the radiation of waves from the jets are determined in this paper from the numerical simulations conducted using a highly stable computational scheme. The simulations show the structure of the jet of super-critical flow is distinctly different from the turbulent flow in the sub-critical jet. The super-critical jet exchanges its fluid with its surrounding through the formation of shocklets while the sub-critical jet by the formation of eddies.