Marginally Stable Inviscid Flows with Critical Layers

Critical layers arise in an inviscid parallel flow when the phase velocity of a small disturbance is equal to the mean fluid velocity. They are characterized by a singularity in amplitude of the disturbance, either when it is self-induced or forced in some way, and consequently the elementary theory becomes invalid in their neighbourhood. They are therefore likely to be of importance in the non-linear evolution of the disturbance if the basic flow is marginally stable so that neutral perturbations are dominant. In this review an account is given of the present state of the mathematical theory of critical layers taking into consideration non-linear effects and also a weak viscosity. Both free and forced oscillations are examined and the basic flow is permitted to include planetary vorticity and also stratification.