Higher-order degenerate points in annular thermoacoustic systems

Annular combustors, such as those typically found in gas turbines for power generation and aeroengines, nominally feature discrete rotational symmetry. Most of the eigenvalues associated with azimuthal thermoacoustic modes in these systems are therefore twofold degenerate, with a corresponding two-dimensional eigenspace. Moreover, as we have recently shown, exceptional points, which are manifestations of defective eigenvalues, are generic features of thermoacoustic systems and emerge from the collision of an acoustic and an intrinsic mode. In a longitudinal, single-flame system, the exceptional eigenvalue has algebraic and geometric multiplicity two and one, respectively. However, in an annular system with discrete rotational and reflection symmetry, lower-order azimuthal eigenvalues -- acoustic as well as intrinsic -- are already twofold degenerate. Consequently, at an exceptional point in an annular system, the defective eigenvalue corresponds to a higher-order degeneracy with algebraic multiplicity four and geometric multiplicity two. We illustrate the formation of exceptional points in annular thermoacoustic systems and discuss implications for modeling and stability analysis.