Equilibrium state of trailing vortices: two-dimensional model of a far-field vortex wake

The equilibrium statistical mechanics of a system composed of a large number of two-dimensional point vortices is employed to describe the vortex system shed from aircraft wings. According to this theory, these higher energy states of the vortex system can only be achieved by segregating the point vortices of like kind into two clusters that descend with a constant velocity. The solution is given in terms of the integral constraints for each cluster: total circulation, center of inertia, and kinetic energy. The negative non-dimensional inverse temperature of the system and the length scale related to angular momentum of a single trailing vortex are obtained versus initial interaction energy of the vortex system. Comparison of the theoretical results with available experimental data shows good agreement between the calculated tangential velocity distribution in the trailing vortex and the data. The flow characteristics for three different wing loads are also compared to emphasize the effect of initial circulation distribution along a lifting wing on the vorticity distribution in the equilibrium trailing vortices.