environment will be confined to a thin layer, permitting the use of a boundary layer approximation.

The basic setup is similar to that of the two-stream problem (see Paper I), with the motion of the [2-D, plane-parallel]{} injected stream predominantly along the $z$-direction, the majority of the variation along $y$, no variation or velocity in $x$, and the point of injection at $y = z = 0$. Now, however, there is no contact discontinuity between the stream and the ambient environment, meaning that the entire system is considered a single fluid. We therefore have less freedom in prescribing the asymptotic characteristics of the jet and the environment; however, this configuration permits mixing between the two media, allowing the outflow to entrain material, which almost certainly occurs in realistic jets.

We can reduce the complexity of equations and by assuming that the interaction between the jet and the ambient medium takes place over a thin boundary layer of thickness $\delta{y}$, thin in the sense that $\delta \equiv \delta{y}/\delta{z}$ is a small number when $\delta{z}$ is a typical length along the jet. In this case, $\delta$ scales in an identical fashion to that derived for the two-stream boundary layer, which can be 