There is no definition of a tornado that has been extensively peer-reviewed.
Other than the Glossary definition, all definitions I've seen, including my own, are not peer-reviewed. Hence none have any formal "approval" except the Glossary definition, which I see as seriously flawed.
A vortex has to meet some threshold intensity at the surface for it to be considered a tornado. However, when we see a debris whirl at the surface, it's not obvious how to go about measuring the wind speeds to see if they meet some wind speed threshold. Lacking a Doppler lidar, the visible evidence of a tight circulation capable of producing a debris cloud at the surface is all we have to go on in ascertaining whether or not a tornado is present.
From my perspective, a tornado is defined
(by any reasonable definition), as a vortex
. A vortex is a kinematic
entity -- a process described completely by the specification of the velocity field as a function of time and space. The dynamics
of vortices -- a description of the physical processes that give rise to the vortex -- probably vary considerably from one event to another, and in general are not very thoroughly known. It makes no sense to me to base a vortex classification system on dynamics when those dynamics aren't known definitively and certainly can't be assessed just by looking at the vortex and attendant storm. We're only marginally capable of saying anything about the velocity field, much less the processes that give rise to it. Instead, I'm arguing that we put some essentially arbitrary (but, hopefully, reasonable) thresholds on which vortices we are going to call tornadoes -- as I am doing in this essay -- from a purely kinematic perspective. When and if the dynamics become well-known and can be determined definitively from available observations, then they can and should be the basis for a revision of the classification system.