We have developed a physical theory for the finding that the most intense laboratory vortex occurs when it is in the form of an end-wall vortex. We argue that the end-wall vortex allows no standing centrifugal waves (i.e., it is supercritical), and therefore, disturbances cannot propagate down from aloft. This allows the low central pressure of the end-wall vortex at the level of maximum azimuthal velocity to be balanced by a central axial jet which jet which accelerates from the lower end wall to this level. This supercritical, end-wall vortex undergoes a transition to a subcritical vortex aloft through a vortex breakdown. We construct a model for the maximum intensity of these vortices by developing a model for the end-wall vortex and by finding the criterion for a vortex breakdown to be in steady suspension above the lower end wall. The model agrees well with previous experimental simulations of tornado-like vortices in the Purdue tornado vortex chamber a steady end-wall vortex adjacent to the... Abstract We have developed a physical theory for the finding that the most intense laboratory vortex occurs when it is in the form of an end-wall vortex. We argue that the end-wall vortex allows no standing centrifugal waves (i.e., it is supercritical), and therefore, disturbances cannot propagate down from aloft. This allows the low central pressure of the end-wall vortex at the level of maximum azimuthal velocity to be balanced by a central axial jet which jet which accelerates from the lower end wall to this level. This supercritical, end-wall vortex undergoes a transition to a subcritical vortex aloft through a vortex breakdown. We construct a model for the maximum intensity of these vortices by developing a model for the end-wall vortex and by finding the criterion for a vortex breakdown to be in steady suspension above the lower end wall. The model agrees well with previous experimental simulations of tornado-like vortices in the Purdue tornado vortex chamber a steady end-wall vortex adjacent to the...