Abstract. The large scale atmospheric vortices (tropical cyclones, tornadoes) are complex physical systems combining thermodynamics and fluid-mechanical processes. The late phase of the evolution towards stationarity consists of the vorticity concentration, a well known tendency to self-organization , an universal property of the two-dimensional fluids. It may then be expected that the stationary state of the tropical cyclone has the same nature as the vortices of many other systems in nature: ideal (Euler) fluids, superconductors, Bose–Einsetin condensate, cosmic strings, etc. Indeed it was found that there is a description of the atmospheric vortex in terms of a classical field theory. It is compatible with the more conventional treatment based on conservation laws, but the field theoretical model reveals properties that are almost inaccessible to the conventional formulation: it identifies the stationary states as being close to self-duality. This is of highest importance: the self-duality is known to be the origin of all coherent structures known in natural systems. Therefore the field theoretical (FT) formulation finds that the cuasi-coherent form of the atmospheric vortex (tropical cyclone) at stationarity is an expression of this particular property. In the present work we examine a strong property of the tropical cyclone, which arises in the FT formulation in a natural way: the equality of the masses of the particles associated to the matter field and respectively to the gauge field in the FT model is translated into the equality between the maximum radial extension of the tropical cyclone and the Rossby radius. For the cases where the FT model is a good approximation we calculate characteristic quantities of the tropical cyclone and find good comparison with observational data.