This makes futile past attempts to extend jet model predictions into the terminal layer phase. In actual discharge situations one or more of the five regimes can occur as asymptotic regimes. Integration across the jet leads to four flux qualities at any jet position s, the volume flux Q, the momentum flux M, the buoyancy flux J and the tracer mass flux Q c . These are summarized in Table 1 as well as the conservation equations for the change along the jet trajectory s in which q and s are the local vertical and horizontal angles, respectively. The turbulent interaction of the buoyant jet with its surroundings is represented by two expressions, the entrainment rate E in the continuity equation and the drag force F D in the momentum equations.
C D represents a drag coefficient.
Over the years there has been considerable controversy over whether a turbulent drag effect is consistent with the ambient flow around an entraining jet. The agreement is satisfactory. For both cases of advected line puff and thermal the entrainment velocity, u e is proportional to the propagation velocity . 3 and 4 show satisfactory agreement even though the data scatter is considerable in these flows with large turbulent elements. Beyond that necessary requirement the entrainment hypothesis, Eq. 2, clearly contains somewhat arbitrary formulations for the transition ranges.