An inviscid algebraic instability for streamwise independent disturbances in compressible flow is found to be related to Ellingsen and Palm’s [Phys. Fluids 18, 487 (1975)] solution for incompressible flow. For compressible flow, the streamwise disturbance velocity, the density, as well as temperature perturbations grow linearly with time. The effect of viscosity on the inviscid algebraic growth is clarified using a rescaling of the viscous disturbance equations, showing the dependence of the viscous transient growth on the Reynolds number.
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Hanifi et al. (1998) studied this question.