Infrared emission by active nitrogen I. The kinetic behaviour of N ₂ (B' ³ ∑ ^- _u )

The boundary-layer equations for an incompressible fluid in motion past a flat plate are examined, numerically and analytically, in the special case when the pressure gradient vanishes and there is a uniform injection of fluid from the plate. In the numerical study the principal properties of the boundary layer are computed as far as separation (x = x$_s \doteqdot$ 0.7456) with a high degree of accuracy. In the analytic study the structure of the singularity at separation is determined. It is of a new kind in boundary-layer theory and its elucidation requires the division of the boundary layer into three zones-an outer zone in which the non-dimensional velocity u is much larger than x* (the non-dimensional distance from separation), a central zone in which u $\sim x*$ and an inner zone in which u \simeq x*. A match is effected between solutions in the central and inner zones from which it is inferred that the skin friction $\tau_0 \sim (\frac{x*}{ln (1/x^*)}^2$ as $x* \rightarrow 0$. A completely satisfactory agreement between the numerical and analytic studies was not possible. The reason is that the analytic study is only valid when ln (1/x*) 1 which means that for the analytic and numerical studies to have a common region of validity, the numerical integration must be extended to much smaller values of x* than is possible at present. It was also not possible to effect a match between the central and outer zones in the analytic solution due to the difficulty of finding the properties of the stress $\tau$ in the central zone as $u/x* \rightarrow \infty$.