Descriptor Techniques for Modeling of Swirling Fluid Structures and Stability Analysis

In this paper we develop descriptor techniques for modeling swirling hydrodynamic structures. Using the descriptor notation we obtain the generalized eigenvalue formulation for differential-algebraic equations describing the spatial stability of the fluid flow. We describe the general framework for spatial stability investigation of vortex structures in both viscous and inviscid cases. The dispersion relation is analytically investigated and the polynomial eigenvalue problem describing the viscous spatial stability is reduced to a generalized eigenvalue problem in operator formulation using the companion vector technique. A different approach is assessed for spatial inviscid study when the stability model is obtained by means of a class of shifted orthogonal basis and a spectral differentiation matrix is derived to approximate the discrete spatial derivatives. Both schemes applied to a swirling fluid profile provide good results. Key-Words: Hydrodynamic stability, Swirling flow, Descriptor operators, Spectral collocation.