THE NONLINEAR CRITICAL-WALL LAYER IN A PARALLEL SHEAR-FLOW

The nonlinear critical layer theory is developed for the case where th e critical point is close enough to a solid boundary so that the criti cal layer and viscous wall layers merge. It is found that the flow str ucture differs considerably from the symmetric ''cat's eye'' pattern o btained by Benney and Bergeron [1] and Haberman [2]. One of the new fe atures is that higher harmonics generated by the critical layer are in some cases induced in the outer flow at the same order as the basic d isturbance, As a consequence, the lowest-order critical layer problem must be solved numerically, In the inviscid limit, on the other hand, a closed-form solution is obtained. It has continuous vorticity and is compared with the solutions found by Bergeron [3], which contain disc ontinuities in vorticity across closed streamlines.