The linear stability of a circular vortex interacting with two plane acoustic waves propagating in opposite directions is investigated. When the wavelength is large compared to the size of the vortex, the core is subjected to time-periodic compressions and strains. A stability analysis is performed with the geometrical optics approximation, which considers short-wavelength perturbations evolving along the trajectories of the basic flow. On the vortex core, the problem is reduced to a single Hill–Schrödinger equation with periodic or almost-periodic potential, the solution to which grows exponentially when parametric resonances occur. On interacting with the acoustic waves, the circular vortex is thus unstable to three-dimensional perturbations.