Properties of a Time-Dependent Nonlinear Viscous Critical Layer

The time-dependent, nonlinear, viscous critical-layer problem posed by Gajjar and Smith is studied analytically and numerically, for various values of the time-dependence parameter µ and the viscous parameter γ_c, to help to complete the understanding of the solution. The analysis concerns the nearly inviscid limit γ_c → 0 which corresponds to increasing disturbance amplitude, other limits for weaker disturbances having been studied previously. On the numerical side, computational results obtained for order-1 values of µ, γ_c are described and are compared with analytical predictions. Particular attention is given to the phase shift produced across the critical layer.