something in that still does not fit.
An airplane in level flight has lift, but its potential energy remains constant, like the computer on the desk (no vertical distance covered, no work done due to vertical forces).
If speed is constant its kinetic energy is constant, too. However, as it is moving forward while being pushed by the engines thrust, there is work done and energy "spent" in a given distance: fuel energy. In the end, fuel energy is being spent to maintain kinetic energy over distance, or fuel power spent over time.
The question is: What kind of power is being spent to keep the airplane level?
Energywise, Who pays all the bills? It seems to me that the engines do.
The airplane remains level but the air pushed down by the wings does not. I mean: the air dragged forward accounts for drag and the air pushed down accounts for lift.
Aside from the air being moved the air is also being heated, oscillated, etc... Energy is imparted to the air in the form of kinetic energy, heat energy, noise... All of that energy comes from the airplane, which maintains its own energy state constant. Therefore it must all come from the fuel.
We could say that the energy used to push air down is the useful energy (creates the lift force). The rest of the energy is wasted in the air. So we can talk about efficiency, in the sense that a wing can achieve the same lift force wasting more or less energy into the air. The more efficient the wing is, the less air is dragged forward or heated, etc...
But what about the vortex? this is air in motion, but if it was to be accounted as drag this motion should be forward. Or do we have to account it as an extra force the engines have to do to pay "wasted energy"?