r-ϕ plot of the radial velocity in units of u_K(R_∗) at t = 5a) and t = 10b) orbits. The velocity in the upper panel, a), has been multiplied by a factor of 2 in order to use the same colormap as below. Both snapshots show the linear stage of the sonic instability and the middle branch in action. The sound waves are propagating toward the inner and the outer edge of the domain in an oblique fashion. The three black lines in panel b) illustrate the wavefronts. The arrows denote the direction of the unperturbed azimuthal flow.