Eliminating spurious eigenvalues in the analysis of incompressible fluids and other systems of differential-algebraic equations

We describe a general framework for avoiding spurious eigenvalues — unphysical unstable eigenvalues that often occur in hydrodynamic stability problems. In two example problems, we show that when system stability is analyzed numerically using descriptor notation, spurious eigenvalues are eliminated. Descriptor notation is a generalized eigenvalue formulation for differntial-algebraic equations that explicitly retains algebraic constraints. We propose that spurious eigenvalues are likely to occur in the analysis of any set of differential-algebraic equations when the algebraic constraints are used to analytically reduce the number of independent variables before the system is approximated numerically. In contrast, the simple and easily