A simple toy model of the advective-acoustic instability I. Perturbative approach

Understand

Some general properties of the advective-acoustic instability are described and understood using a toy model which is simple enough to allow for analytical estimates of the eigenfrequencies.

• The essential ingredients of this model, in the unperturbed regime, are a stationary shock and a subsonic region of deceleration.
• For the sake of analytical simplicity, the 2D unperturbed flow is parallel and the deceleration is produced adiabatically by an external potential.
• The instability mechanism is determined unambiguously as the consequence of a cycle between advected and acoustic perturbations.