Dynamic sealing device for an aircraft turbomachine, comprising two rotors (3, 8) which are configured to rotate about the one same axis (A) and different speeds, the said rotors extending at least in part around one another and dynamic sealing means (14) being mounted between the said rotors, characterized in that: —the said sealing means comprise annular rings (38) extending about the said axis, these rings being mounted with the ability to slide on a first (3) of the said rotors, in a radial direction with respect to the said axis, and being able to bear radially via their external periphery against a second (8) of the said rotors which at least partially surrounds the said first rotor, and in that it further comprises: —oil discharge means comprising an annular cavity (44) formed in the said second rotor, the said annular cavity opening radially towards the inside in the vicinity of the said sealing means and being in fluidic communication with oil passage ports (45) formed in the bottom of the cavity and passing through the said second rotor.