Accurate determination of stability characteristics of spatially modulated shear layers

Abstract

We present a method for accurately determining the stability characteristics of spatially modulated shear layers. The algorithm can handle arbitrary commensurate states, which are not accessible to classical direct-numerical-simulation-based approaches. It uses spectral discretization of the field equations to handle field modulations and the spectrally accurate immersed boundary conditions method to handle the geometry modulations. The algorithm can deal with pattern interaction effects driven by modulations of different physical origins. Various tests demonstrate that the algorithm delivers spectral accuracy for eigenvalues and eigenfunctions. The algorithm can be easily extended to analyse many sources and patterns of modulation with minimal commitment to the user's time.