A one-channel time-reversal (TR) experiment is performed inside a rough reverberating cavity in the presence of a rotational flow. The amplitude of the TR wave is plotted versus the distance between the TR channel and the initial source: when they coincide, it exhibits a "time-reversal enhancement" (TRE). With no flow, the TRE is the same as the coherent backscattering enhancement (CBE). But contrary to CBE, the TRE peak is shown to be insensitive to the breaking down of reciprocity due to the flow. This new effect of weak localization is sustained by a diagrammatic approach.