FREQUENCY SELECTION AND GLOBAL INSTABILITIES IN 3-DIMENSIONAL WEAKLY NONPARALLEL FLOWS

The temporal evolution of global modes is studied, which are time-harm onic solutions of the linear disturbance equations, subject to homogen eous boundary conditions in all space directions. As basic flow we con sider weakly nonparallel three-dimensional shear flows. A necessary co ndition for the existence of a global mode is the presence of at least two branches of the local dispersion relation and a location where th ey coalesce. It leads to a mode coupling in a neighborhood of that poi nt. To analyze the mode coupling the uniform asymptotic description of Kravtsov and Ludwig is employed which also yields a general formula f or the global eigenfrequency.