Field theoretical prediction of a property of the tropical cyclone

The large scale atmospheric vortices (tropical cyclones, tornadoes) are complex physical systems combining thermodynamics and fluid-mechanical processes. The well known tendency of vorticity to self-organization, an universal property of the two-dimensional fluids, is part of the full dynamics, but its description requires particular methods. The general framework for the thermodynamical and mechanical processes is based on conservation laws while the vorticity self-organization needs a variational approach. It is difficult to estimate to what extent the vorticity self-organization (a purely kinematic process) have influenced the characteristics of the tropical cyclone at stationarity. If this influence is substantial it is 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 - Einstein condensate, cosmic strings, etc. In previous works we have formulated a description of the $2D$ vorticity self-organization in terms of a classical field theory. The field theoretical (FT) formulation finds that the quasi-coherent form of the atmospheric vortex (tropical cyclone) at stationarity is an expression of the Self-Duality. 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.