What can the kinematic complexity of astrophysical shear flows lead to

We develop a method for investigating waves and instabilities in astrophysical shear flows with complex kinematics. Using new tools, we find an unexpected richness in the spectrum of compressible fluctuations sustained by such a flow. The principal characteristic of the revealed exotic phenomena is their asymptotic persistence in the absence of viscosity. "Echoing" as well as strongly unstable (including parametrically driven) solutions are identified. Examples of astrophysical shear flows with nontrivial velocity structure where these method and results can be applied are also discussed