Frequency selection and global instabilities in three-dimensional weakly nonparallel flows

The temporal evolution of global modes is studied, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. As basic flow we consider weakly nonparallel three-dimensional shear flows. A necessary condition for the existence of a global mode is the presence of at least two branches of the local dispersion relation and a location where they coalesce. It leads to a mode coupling in a neighborhood of that point. To analyze the mode coupling the uniform asymptotic description of Kravtsov and Ludwig is employed which also yields a general formula for the global eigenfrequency.