Symmetry analysis in linear compressible hydrodynamic stability theory

We present a unifying solution framework for the linearized gas-dynamical equations for a two-dimensional (2-D) linearly-sheared unbounded homentropic compressible flow using Lie symmetry classification. The full set of symmetries that are admitted by the underlying system of equations are employed to systematically derive three distinct invariant Ansatz functions, which unify the existing ones for normal mode, Kelvin mode analysis, as well as a novel approach. The latter approach considers modes that are localized in the cross-stream and periodic in the streamwise direction and travel on parabola shaped curves at constant velocity in the cross-stream, while being accelerated constantly in streamwise direction by the underlying base flow