Is Biot–Savart law physical in aerodynamics?

Question

Biot–Savart law comes from electromagnetics theory. Vorticity behind the wing(in the wake) induce downward vertical velocity upstream of the wing, so effective AoA of the wing is reduced.

Is this really mechanism what happend in real fluid(air)?

Answer 1

No.

You start from wrong premises. Vorticity adds an upward vertical velocity ahead of the wing. This is called induced angle of attack. You cannot focus on the free vortices behind the wing without including the bound vortices within the wing. While the free vortices would indeed add a downward vertical velocity between their cores, the bound vortices are dominant for the induced velocities ahead of the wing and cause an overall increase in the angle of attack.

Answer 2

In subsonic flow, the differential equations are elliptic -- this means that everything influences everything. In supersonic flow, the equations are hyperbolic -- which means that disturbances only move downstream, nothing downstream can influence anything upstream.

If you think of a simple 3D lifting wing model -- a single horseshoe vortex, then yes, the two trailing vortices are the source of induced drag and all the 3D effects.

A super-simple 2D lifting airfoil model is a single point vortex placed at c/4. When extended to 3D, that would be the bound vortex of the wing -- the 'crossbar' between the trailing vortices.

The bound vortex causes an upwash ahead of the wing (and a downwash behind it). The trailing vortices cause a downwash between them - and an upwash outside of them. This region of downwash extends in front of the bound vortex - but is weaker than the bound vortex influence.

The trailing vortices cause the lift distribution to vary from its peak at the root to zero at the tips.