Vortices represent kinetic energy and they don’t occur spontaneously in the atmosphere. The law of conservation of energy requires that a force must act on the atmosphere to cause a vortex. In the case of trailing vortices behind an airplane the generating force is the reaction to the induced drag on the airplane. If the induced drag on an airplane increases by one percent, the rate at which energy is added to the trailing vortices also increases by one percent. Therefore the energy in the trailing vortices is known once the induced drag on an airplane and its true airspeed are known.
But what is dangerous to the trailing aircraft is not the total energy of all the trailing vortices coming off the aircraft, it is the energy that is still organized in a vortex miles behind the aircraft. A quick look at the outboard edge of deployed flaps in moderately high relative humidity conditions will show that a very prominent vortex is generated there. By the same quoted law of conservation of energy, obviously the wing tip vortex is reduced by the addition of flaps to allow for the formation of the second vortex at the flap tip. This last is sarcasm, as obviously the total changes, but I think you can see where this is going. In order for wake turbulence to be dangerous, it has to stay organized as long as possible in time and space.
Perhaps the authors of 90-23F know something that aerodynamicists don’t. Aerodynamicists would be willing to accept the knew knowledge if only the authors would divulge what it is.
It's not that there is any "knew" math knowledge to be had. I think what the misguided FAA authors of AC 90-23F are talking about is the
actual ability of
observed vortices during several
actual passes in different configurations to pose a danger to trailing aircraft. No math regarding the induced drag efficiency involved, just bigger wing tip vortices for the next plane.