None of my business really, but it seems to this non-expert that some writers are confusing transient effects with a new stable configuration.
When lowering the flaps, instantaneously the momentum of the aircraft is maintained (no infinite force, so no immediate change in velocity – just accelerations that start). If the aircraft is kept pointing in the same direction, at the moment that the flaps are lowered:
1. Alpha at the inboard/flap section is immediately increased, if alpha is defined as the angle between the airflow and the chord from leading edge to (now lower) trailing edge. Hence inboard contribution of lift is transiently increased. If I do this in my glider, the immediate effect is to bounce it higher than it was, or reduce the rate of descent, very briefly – I can feel it happen. A sensitive accelerometer would display it as a transient effect.
2. Alpha at the outer/tip section is not changed instantly – airflow, attitude and wing section are not changed instantly.
What happens next depends on the pilot’s actions. If the nose is lowered to arrive at the same stable speed as before, after things settle down, alpha is higher inboard, lower outboard; overall Oswald efficiency (a term I had not heard before – thanks, D.) is lower as Dolphin says, and more energy is transferred to the atmosphere generally. The energy comes from more power expended or a greater rate of descent/expending more potential energy. Ultimately, that manifests itself as the vortices, as I understand it – the ultimate effect of a lift-producing wing passing through air is to add rotation, which appears as the vortices. More energy expended, stronger vortices. Unless someone has found a way round the laws of physics.
If the nose is not lowered, after things settle down a new phase of flight is entered with possibly different speed, certainly different alphas at tip and inboard, and the maths is too complicated for me to summarise. (But anyway, when flying, I can’t tell the induced drag – it is total drag that produces effects that the pilot sees.)
Chris N.