NON-LINEAR STABILITY OF A TWO-DIMENSIONAL STAGNATION FLOW.

A slightly nonlinear case of stability is treated when the non-dimensional amplitude A//o of the dusturbances in a two-dimensional stagnation region of a cylindrical blunt body is not so large that the derivative of A//0**2 with respect to a non-dimensional time tau can be expressed as dA//o**2/d tau equals 2A//o**2( alpha //o plus alpha //1A//o**2) where, alpha //o and alpha //1 donte the respective growth factors of the first and second degrees. The mutual combination between the signs of alpha //0 and alpha //1 has an important significance for the problem of nonlinear stability. The results of alpha //1 less than 0 is obtained by determining the value of alpha //1 such that the integration of the kinetic energy involved in the disturbances becomes minimum up to the higher order of magnitude. This results suggests that the flow in the stagnation region reaches the state of super-critical equilibrium when the Reynolds number exceeds the critical value.