GLOBAL LINEAR-STABILITY ANALYSIS OF WEAKLY NONPARALLEL SHEAR FLOWS

The global linear stability of incompressible, two-dimensional shear f lows is investigated under the assumptions that far-field pressure fee dback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e. that its streamwise d evelopment is slow on the scale of a typical instability wavelength. T his implies the general study of the temporal evolution of global mode s, which are time-harmonic solutions of the linear disturbance equatio ns, subject to homogeneous boundary conditions in all space directions . Flow domains of both doubly infinite and semi-infinite streamwise ex tent are considered and complete solutions are obtained within the fra mework of asymptotically matched WKBJ approximations. In both cases th e global eigenfrequency is given, to leading order in the WKBJ paramet er, by the absolute frequency omega(o)(X(t)) at the dominant turning p oint X(t) of the WKBJ approximation, while its quantization is provide d by the connection of solutions across X(t). Within the context of th e present analysis, global modes can therefore only become time-amplif ied or self-excited if the basic flow contains a region of absolute in stability.