Numerical illustration of the global and local stability and instability of the constant spatially developing 1D gas flow

Abstract

In this paper different types of stabilities (global, local) with respect to instantaneous perturbations and permanent source produced time harmonic perturbations are numerically illustrated in case of a constant spatially developing 1D gas flow. Some types of instabilities (global absolute, local convective) are also illustrated. For this purpose the 1D Euler equations linearized at the constant gas flow are used. It is illustrated for instance, that the constant gas flow is globally absolutely unstable with respect to some instantaneous and some permanent source produced time harmonic perturbations. The locally convective instability is also illustrated with respect to some instantaneous and some permanent source produced time harmonic perturbations.

Keywords

• global/ local stability/ instability
• spatially developing gas flow