Balancing stability and sensitivity in hypersonic boundary layers using input-output analysis

We apply Input/Output (I/O) analysis to study instabilities of hypersonic boundary layers over sharp and blunt cones. Compared to conventional stability analysis, I/O analysis represents a paradigm shift from a local view to a global view of instabilities. Based on standard techniques from linear systems theory, I/O analysis uses the resolvent operator to find the total system frequency response to external excitation. We first verify that the global view provided by I/O analysis is correct by comparing its results to well-known results corresponding to the development of second mode instability on a sharp cone. We then show that I/O analysis seamlessly handles the complex flow created by the tip of a blunt cone that otherwise violates the assumptions underpinning traditional stability analysis. Because of its global scope, I/O not only captures second mode instability, but also identifies additional instability mechanisms on blunt cones that traditional stability analyses have been unable to predict. We also demonstrate how I/O analysis incorporates sensitivity information to the disturbance input location, which provides a physical measure of the minimum amplitude of disturbances that can lead to flow transition.