Here's another attempt to help people understand why certain theories which
are intuitively appealing are doomed to failure.
People like nice, simple, linear theories. The problem is, fluid dynamics
is nonlinear -- highly nonlinear.
Consider two airplanes with reasonably long wings, initially flying in
formation, wingtip to wingtip. Then they move apart, maintaining constant
airspeed at all times. This produces an increase in the induced drag
force. This is fundamentally a nonlinear effect. It is not a small
nonlinearity; there is (to a good approximation) a 100% increase in
induced drag.
Any theory that involves only a simple "throw something down" process is
too simple to provide a passable description of induced drag.
I wish I could offer you a nice linear theory of induced drag. But I
can't. Mother nature won't let me.