On multidimensional global eigenvalue problems for hydrodynamic and aeroacoustic instabilities

The present eort discusses multi-dimensional eigenvalue problems as applied to the solution of hydro-dynamic and aeroacoustic instability problems on complex geometries. As a demonstrator, global linear instability analyses of steady laminar ows on an elliptic cone in compressible ows are monitored; one such ow, obtained using a standard aerodynamics solver, is presented in gure 1. Flows on this geometry are intrinsically three-dimensional; as a matter of fact the three-dimensionality of the geometry of the elliptic cone accounts for the departure of the laminar-turbulent transition process from the fairly well-understood scenarios on circular cones 1 and other axisymmetric bodies of revolution. Shedding light on the essentially three-dimensional transition process on the elliptic cone provides motivation for several recent experimen-ta