Searching convective/absolute instability boundary for flows with fully numerical dispersion relation

Abstract

The numerical aspects of finding a complete boundary separating regions of convective and absolute instabilities are discussed in the example of mixed convection flow. The dispersion relation associated with the flow is fully numerical and thus the problem of distinguishing its branches in a complex wave number/frequency space arises when the spatio-temporal instability theory is used to analyse the flow. This paper suggests an algorithm to resolve such a difficulty and applies it to obtain stability results for a wide range of physical parameters governing the example flow.