Originally Posted by
gesres
The changing relative wind on the vertical stabilzer causes the aircraft to yaw in the new direction of movement.
Just to provide a reference to avoid the "hot air" syndrome, I refer to "Fundamentals of Flight" by Richard S. Shevell, p. 323:
When the airplane is accelerated sidewise in a turn, the directional or weathercock stability will rotate the airplane about its vertical axis automatically to keep the airplane pointing into the relative wind. Therefore, turns can be made with ailerons only. The airplane always has an angle of sideslip in such a turn to cause the directional correction. This increases the drag, a condition that can be avoided by use of the rudder to yaw the airplane at a rate that keeps the airplane always headed into the relative wind during the "coordinated" turn.
This rudder, by the way, is necessary regardless of the existence of adverse yaw.
Actually, though, the aircraft is more than just yawing, it's also pitching throughout the turn in order to keep itself aligned with the relative wind. The greater the bank angle, the more pitching that is occurring with respect to the yawing. The mix of pitching and yawing is contained in these formulae:
rate of pitch = Ω cos(θ) sin(φ)
rate of yaw = Ω cos(θ) cos(φ)
where Ω (omega) is rate of turn, θ (theta) is pitch angle, and φ (phi) is bank angle.
(source:Elements of Airplane Performance, Ruijgrok, p. 304)
As you can see, in a flat turn, it's all yaw, no pitch; in a 90 degree banked turn, it would be all pitch, no yaw. Both the yawing moment and the pitching moment are produced by the natural weathercock stability of the airplane.