Similarity equation for a two-dimensional laminar plume
= Similarity equation for a two-dimensional laminar plume
With $u=-\psi_y$, $v=\psi_x$, $\eta=y/\Delta$, and $\psi=U\Delta f(\eta)$, the plume boundary-layer equation reduces to
$$
f'''+\frac15(f')^2-\frac35ff''=\delta(\eta).
$$