Acoustic time-reversal invariance is broken when the propagating medium contains a flow. This effect is taken advantage of to achieve a new way of characterizing the vorticity field of a flow with a double time-reversal mirror (TRM). The double TRM is made up of two transducer arrays surrounding the flow. The time-reversal process is performed between the two arrays: When one array emits, the other one receives, time-reverses, and re-emits the acoustic wave. In the absence of flow, time-reversal invariance insures that many back and forth propagations between the two arrays do not modify the emitted wavefront. In the presence of flow, the acoustic wavefront is distorted through the flow. This distortion is related to the amplitude and size of the vorticity field and is often too small after one crossing to be observed experimentally. In order to amplify this wavefront distortion, several back and forth propagations are imposed on the acoustic wave through the flow between the two arrays. The greater number of crossings through the vorticity field induces an amplification of the effect of vorticity on the acoustic wavefront. This effect can then be easily measured and provides the vorticity characteristics even for flow with a small vorticity field.