Advances in global linear instability analysis of nonparallel and three-dimensional flows

Abstract

A summary is presented of physical insights gained into three-dimensional linear instability through solution of the two-dimensional partial-differential-equation-based nonsymmetric real or complex generalised eigenvalue problem. The latter governs linear development of small-amplitude disturbances upon two-dimensional steady or time-periodic essentially nonparallel basic states; on account of this property the term BiGlobal instability analysis has been introduced to discern the present from earlier global instability methodologies which are concerned with the analysis of mildly inhomogeneous two-dimensional basic flows. Alternative forms of the two-dimensional eigenvalue problem are reviewed, alongside a discussion of appropriate boundary conditions and numerical methods for the accurate and efficient recovery of the most interesting window of the global eigenspectrum. A number of paradigms of open and closed flow systems of relevance to aeronautics are then discussed in some detail. Besides demonstrating the strengths and limitations of the theory, these examples serve to demarcate the current state-of-the-art in applications of the theory to aeronautics and thus underline the steps necessary to be taken for further progress to be achieved.